[{"run_id":"20260906T231458-5fdd2fff","semester":"1272","observed_at":"2026-09-06 23:14:58.172943+00:00","record_version_id":"a15e576e2272c977f63a5b46d67e0172559f716fd83bfbcc9c2a7e2a4a197ca5","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"20260907T155543-ce3781c4","semester":"1272","observed_at":"2026-09-07 15:55:43.033547+00:00","record_version_id":"a15e576e2272c977f63a5b46d67e0172559f716fd83bfbcc9c2a7e2a4a197ca5","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-03b0bbb9723907cf3d1b41cf0bb34837dc398e42","semester":"1262","observed_at":"2025-04-16 05:20:33.104844+00:00","record_version_id":"9181428882f70ad1cc4bf31c4149c4401e9f4b524ef17a49f5221be2e2d0e487","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0837245627eb714ae6bb0375f7abe8f41042011f","semester":"1262","observed_at":"2025-04-16 05:20:33.104844+00:00","record_version_id":"9181428882f70ad1cc4bf31c4149c4401e9f4b524ef17a49f5221be2e2d0e487","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-08c92e359bbbc110b0778b7e0b15d6f40000e6b1","semester":"1262","observed_at":"2025-08-21 07:05:14.730696+00:00","record_version_id":"dc4f41b0dadd9e40dd1c47f2d5a5592ab12de49ec651122ac6893b658e8eff7c","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0944d76440dc778fbb89626058c10451009ce9c6","semester":"1262","observed_at":"2025-05-21 03:36:18.194118+00:00","record_version_id":"44f3f2ce1e1fe5192fd3ed371261261fa7e95ebd711ea5ebd887ecf81f2c515a","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0a7f4bce29c816ef4d3d71b4eb8a2a3e15e33cc1","semester":"1262","observed_at":"2025-06-18 20:04:02.695444+00:00","record_version_id":"05a10db0fc8508539ab7b3b2eda9741ec6e18acbc0b3873741885a1fe5587ac1","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0ab917f827a7de22ebdc1087114d377a31c4687b","semester":"1262","observed_at":"2025-05-22 02:11:02.531191+00:00","record_version_id":"61c3dc9fe63303d37b59590b11aec839d6feb0e58db552d44488f6627e8ce5fc","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0c40ecab4b6db9333d1f18aef816e3ee659e300c","semester":"1262","observed_at":"2025-05-25 18:02:34.797617+00:00","record_version_id":"d842f068e8dd325aa85dc7bf6f9b8161becfebd7323718432a556db363a52163","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0cb4d29a588ec7f11c7e00b7cf5dc3a0d23d0349","semester":"1266","observed_at":"2026-01-22 01:00:26.555427+00:00","record_version_id":"13d3fc74859ea82b740f227988e42ba4a3519266eb64c93efdd125914e8d26ae","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-11c30ec39e91498cbfcf3a923c53a4b03e387280","semester":"1262","observed_at":"2025-07-20 04:58:26.847117+00:00","record_version_id":"5e457a91dbf6d6bef17f0e3acd21354cdf9e1edf874992fed0bdaf4131751d5e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-13cd500edf2587e9a3428f326253738fbea965ea","semester":"1264","observed_at":"2025-12-14 04:50:04.653658+00:00","record_version_id":"33c4c42b7171b3705e12f946da95a5c936e18ae134ad6347b85e61eb2b894ead","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-1da08b2de39f05e6bc877c189fc2fd6eeda563f5","semester":"1262","observed_at":"2025-07-01 00:03:56.707251+00:00","record_version_id":"5f6efeb7f186413e288e3d3bc385160c6038592b03afc9346bb760dce7ea43be","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2031af47efe133b0e7877f433286ff07385afc41","semester":"1262","observed_at":"2025-07-02 20:16:45.749584+00:00","record_version_id":"2d9296dd58e4696799d33b2d5efb1fdbd8bcccd4eb5fd8f7fc0fb38334091257","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-238eba6f32fbc30407f616dd0628ff02a2a824dd","semester":"1262","observed_at":"2025-08-17 05:15:07.788352+00:00","record_version_id":"416721f8693e58c2d9a627aaf409f21b9be4e00244f4da5e2eedc6838b2b9325","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-25f0ff56bc4d80f8a8afa1a0bcce8dae6fddb5e5","semester":"1262","observed_at":"2025-05-25 17:20:25.942090+00:00","record_version_id":"0582dce324bc23bb119435d218bb037315885dacf14efbda8e61e03aa8424bf5","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2923f91826ce253b7aeefa9f75b4a39fe4c80ff0","semester":"1262","observed_at":"2025-08-10 05:10:25.938416+00:00","record_version_id":"df90e916a2028f2de02002950ea2e81c6018b5d36352a0990e831931d0f9e19d","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2a05214a4023e0157fa6f7d188c85308f714176c","semester":"1262","observed_at":"2025-09-07 04:56:38.255315+00:00","record_version_id":"ade75be4fe3ef997efaaeb955533ef309d7ccf08eb03eca54cfbc9a5a00d3d24","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2b1b8e39131de92b94620b25c5bbb25690efed4c","semester":"1262","observed_at":"2025-06-01 07:54:53.913454+00:00","record_version_id":"b26bcb4b943b481b07a00e5f5c0d61b8b371250c5553a28aed8bcfeeec03e215","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-33a1225644e5a5855d60f66e65413946e72fedf4","semester":"1262","observed_at":"2025-06-22 01:52:05.152650+00:00","record_version_id":"8d36be0cdb13fca2e142b3475e7fd7a378603bb0deaa4eed672af1f4a3466fc9","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3b89c83dbf5208e13756184de1f2b2d0c09af35f","semester":"1262","observed_at":"2025-06-30 06:40:10.235522+00:00","record_version_id":"4d2f881439701797e44cbce3011bc87e9ac3e18725d36d255df7109df8e35290","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3c3eebf7f35c39364b445a2fa5a112ce28dbb4a1","semester":"1262","observed_at":"2025-06-01 17:03:59.062985+00:00","record_version_id":"3abdc3e5d3ef25ae0a5b0f298052c6bf4b6cafa38b033f92fc1ddeeee5cde825","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3fa4dd71391f1c9cf4ab2216680bbc428689f92d","semester":"1262","observed_at":"2025-05-25 01:15:58.180530+00:00","record_version_id":"dc3983de306b45bb5250185ee7d231f8d4af1ce2e371d3e5c4fb932af58a9486","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-4040aa216da722a34483f68fc1e129ea571ae08d","semester":"1262","observed_at":"2025-06-01 07:27:39.695506+00:00","record_version_id":"0522f981a4272a30c8f8057964b23090b6fde4bcf9d12113862c025bebd199ac","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-454d53cd690294459f8ad0793cc3ed562060e56c","semester":"1262","observed_at":"2025-05-25 01:34:00.536004+00:00","record_version_id":"53ac29c75324ce6f1149bdaaf6412c343d9cf82daacc29d03fab0e6cd028cde3","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-486f091e051fdb4ccdb80ee7b4fb0a5814510324","semester":"1264","observed_at":"2025-11-16 05:32:31.273726+00:00","record_version_id":"260d35c9104176dede4854aa7f5a4d06f265b500b06699f27e9ac2e3abcc3b7a","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-50393cfc5fd5598d4f4731ef1919f2ff53af07d9","semester":"1262","observed_at":"2025-06-30 06:05:57.438846+00:00","record_version_id":"a44a7c6441512c27db5146b21f19c403b9be0d10b444b3f4c41f1c1a00955edf","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-50f6947786b208c800db8bbd0cec84a8f0f187d2","semester":"1262","observed_at":"2025-06-02 03:49:42.915428+00:00","record_version_id":"39897798db58ff792da70c16adedaae61be8f6a5d04dbfda75e6ce314a1511b2","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-51d86ed4082dced3803c295419b0ec8440942016","semester":"1264","observed_at":"2025-11-12 04:50:41.141307+00:00","record_version_id":"2f22aa437347279eff931184ede67ad771d9b3cb88bb099b3a3ececd2835a49d","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-53101bd1c10db0d00d094e4c9154d4c244ff23d9","semester":"1262","observed_at":"2025-10-05 04:58:05.366968+00:00","record_version_id":"c267382ea62152a25b5983237ab24379cbbbb0c329b9f82320fbb75903bffe50","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-58751151c564e11c5cb8aedd3a2d3527c22f73eb","semester":"1262","observed_at":"2025-06-01 06:59:01.536576+00:00","record_version_id":"eab2c2a274ed952aeab9732a3532d346052c9600f14811ac6ba29d41c12616ea","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5c4c8d3701a333ba4ddadef7d0b5dde8440fcdf0","semester":"1262","observed_at":"2025-06-01 01:57:51.256704+00:00","record_version_id":"51544bbb34b338200b0f50f6795ac27a21ade4652a9b0f5b5636c3760d5a1bb0","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5d20d9f81651d3c83fcaa2fd10870ce6e5d5a685","semester":"1262","observed_at":"2025-05-21 16:48:48.484741+00:00","record_version_id":"8357299eccf71d422a8ca544604e75fe04b21dfa9450d8de930da28b63a0f048","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5feaebf2ab37051c86ad360cc0fa0d7e0e2ea295","semester":"1262","observed_at":"2025-05-24 15:58:23.378859+00:00","record_version_id":"ca6828b70227c38854e61f44f6fb2ce8d0b34a84a1c5b6ff1b42fc09bb5c0490","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-60949965544fce098cc006354e201149005fb77b","semester":"1264","observed_at":"2025-10-26 05:07:14.077864+00:00","record_version_id":"ab504fa7cb13dd1a41f5ee327282226a72fd10dbd6c5d4484c44e5bc842b377b","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-639225ac3addf8522f1d30cb4fe26054ea7f8c49","semester":"1262","observed_at":"2025-06-01 08:14:42.497608+00:00","record_version_id":"d1932a44283350ff45a9d029e9d06a2b339e4e9ebefecd401a619ab131a951ce","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-64093b17b3a9c67a41aa33eb37adb53ec38df714","semester":"1262","observed_at":"2025-05-22 02:11:02.531191+00:00","record_version_id":"b64851703d289018430064c7d2455bde6269d4ec2940de6381839d2d355b3dde","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-6885b56099f55e08aa0205546369fb0381d50e13","semester":"1262","observed_at":"2025-07-13 04:59:22.367394+00:00","record_version_id":"9247f43fa63e974d299cd31fc52c324341ab27fb199f095b674b9440666bba6e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-69d4b2b16e8268f75b6390b3a0e2ce8bf73999da","semester":"1262","observed_at":"2025-06-30 03:21:29.925498+00:00","record_version_id":"ccdc7ef67131900288e6c370fe3bb45e36ab548d07c44f507f022265dd1a3d0c","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-6b29c3e0673b2f9a736d2363db5409e03d5b3ed4","semester":"1264","observed_at":"2025-12-03 12:33:41.418072+00:00","record_version_id":"0b528fa2575701934eab8d556b8dd3dbd3c891ec34b116ed446ad54e711dab39","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-73259984748de484976ef2ad56ad7ab3d4cb4518","semester":"1262","observed_at":"2025-06-26 08:27:56.461216+00:00","record_version_id":"ed9e75c84ef50387b576cc920093d866504fea6ef03fed9beb9611f26776aa50","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-741602fbc6252c232a0b9e6bc1a9ae3101625f5a","semester":"1262","observed_at":"2025-06-30 22:49:32.522034+00:00","record_version_id":"c0da6cbdc10f4f9cc0664b69e267dc7dd2315eecb106b6379829b3149d85f72e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7774f45558276ec29bf626e58fffb4a27bdbb2a9","semester":"1264","observed_at":"2025-11-01 11:49:36.359151+00:00","record_version_id":"8463f51617a04f9338bfaf5557d65977dc69f97895666b00bf0c8edd751161e3","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7ab7c5e783fc8ebef8b8ee8cea019ee37a72ce74","semester":"1262","observed_at":"2025-09-28 04:58:07.340658+00:00","record_version_id":"28284eaa9411b8dfb7c1c60fa859c468e3d63c156815c48c545b5175f5776cea","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7b2f22d83ea05055ab90dcb77dc802382cccc6f7","semester":"1262","observed_at":"2025-05-21 17:56:46.096741+00:00","record_version_id":"605579eb891d7bdab4b50f985a3ec4e55676fe82698688e3d041346c83821526","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7ca1175502be18eb51f7b016818a884a43fd4ebb","semester":"1262","observed_at":"2025-07-29 06:28:23.644795+00:00","record_version_id":"1563eb3e5c9fbdc2a2bf3dd927a50efdeddf9172718fb53d7a2f0fdaa776a83e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7d8cee5e42602ad9ba5dc0322085af2fa0dffaac","semester":"1262","observed_at":"2025-05-22 01:15:19.291664+00:00","record_version_id":"aebbe946265ff758a0fe3c17d8859165152b02b7156d38e2dd97cd06df6b8b3c","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-81a0d6a7f668c98c59bd05fa988aa079c5ad1f68","semester":"1262","observed_at":"2025-05-31 07:49:50.419452+00:00","record_version_id":"fd24aa1472d969ad72c422d80a7df5939f0b921516503b3a0cc2bcf9548c9b11","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-82f31c08c746a214872494cde6ecaeb9330441b4","semester":"1262","observed_at":"2025-06-17 21:26:08.547156+00:00","record_version_id":"27b0eec242e4d88558cc4887cf102246b32b45436c06714c214e8ed5f79682c3","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-84c248343c5a99ab42c5616c594812a5e3e31cbb","semester":"1262","observed_at":"2025-07-04 06:00:07.487827+00:00","record_version_id":"019324e1f0a1a0569fb2789b01443221a216d95d7ce1f0541104851c7bfd4cc9","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-86334e7275e315853287e8580c35456c68df800b","semester":"1262","observed_at":"2025-05-22 06:53:03.336354+00:00","record_version_id":"8c3797f61e41030a06e86679103bb3876e035697d76d76e99f8e077844d0665c","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-8686dc1664f93a6c05f50321410961b39b12f91b","semester":"1262","observed_at":"2025-05-28 10:17:41.595894+00:00","record_version_id":"6f54b19dacfa104ce8e7ad3586d5c3033eea94a779d05a1af71cae2bc1d43edb","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-86d941366886c9a14a2581c04e20d0bdd25e1b02","semester":"1262","observed_at":"2025-08-31 04:54:14.656039+00:00","record_version_id":"6dc8e8f84b4b372b95926dce608e05420c34309a6870f3fa8725f71a2473ddc3","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-8ba1d2e6cfbb1525b4f9f769ec164fb6ad0f237a","semester":"1262","observed_at":"2025-06-02 05:22:45.010398+00:00","record_version_id":"4d633403df9564989c88117eaf95f505324841a0bc677513f8f9e67a78458268","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-90e5aa456689a3b222016c05c319bbcd0bddd453","semester":"1262","observed_at":"2025-05-25 02:00:10.037905+00:00","record_version_id":"e54e478cacc917c76e43b79480b14c4135b03eee5b92d202ec87831052decd45","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-92d960aa7e4cd6e4c9ac8b2e232092904038e9e4","semester":"1262","observed_at":"2025-06-08 01:50:46.451351+00:00","record_version_id":"beb4a4cd8c8efa122924cc817b6f92b6c0ae7b4965c2bdb5d9d91bd6dd080159","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-94002ae588a8f71eca6d64105f2e603e8587293b","semester":"1262","observed_at":"2025-05-21 09:01:16.021508+00:00","record_version_id":"0294f127a0924d9bf1da02d2398eac6e6f866bdda652a3ff552b9ebe1dd744fa","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-9dd575e013c5c6e000ab3ad2d1288cc1dd9c96dc","semester":"1264","observed_at":"2025-12-21 04:47:46.589081+00:00","record_version_id":"1079fae945020600ccb5e92707ec03242d21eb95820a5ac23f7047c3916cb2ad","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-a1ea26ed78cbd6e94bc3221e50a6ed9b6bf43871","semester":"1262","observed_at":"2025-05-25 09:16:55.180581+00:00","record_version_id":"9758fcfab164fdd3bd56f34f902074574ccd892ad76f134e56ad58f9eb82971e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-a76a3505853d5ea9c13bb98472b87361d469e2ee","semester":"1262","observed_at":"2025-05-28 18:03:41.793846+00:00","record_version_id":"7a5e4e1673e76fd0154b5afbc3693365bb2095dcbde4ac62c0591b6bda50f185","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b285d591f6acf3aa1910e02edc297664db86eb8c","semester":"1262","observed_at":"2025-06-10 22:48:22.460295+00:00","record_version_id":"cadcef07fb2cad84d6debc44c93dee18afbe2e07538aada71a52989489b204f2","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b79af756e4f00ba98231feb859ed8e98239eb811","semester":"1262","observed_at":"2025-05-22 02:47:56.931581+00:00","record_version_id":"21fe63ecb3b5b2ec96b983cfcb1c08b44ea56ead34a19f687756c616c20a7060","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b89e05b94730c6471439082d9279c0a834a4aeec","semester":"1262","observed_at":"2025-08-26 20:25:42.325239+00:00","record_version_id":"246b133c91bee6f556f0449e6cd10ac56d9c0382cafbd4b41fc5511519c0fbad","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b9279a12d1f2688df9e556183c94d41a89e431dc","semester":"1262","observed_at":"2025-07-06 01:49:47.203835+00:00","record_version_id":"f59c113a7c0f5fa046779f5e5574334ebeb8a74153824598db7d41c72266c98b","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-bbdc905e96cc681a5e9a8b02c795b682206e36d1","semester":"1262","observed_at":"2025-06-25 08:02:45.445730+00:00","record_version_id":"9ae9909c44205b09a3f45c4f18cc6861b28e2d94a64eb1bec8ebf3109b5bb4ac","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-bde225b5243a13d81827aa173e39c78a652b54a0","semester":"1262","observed_at":"2025-05-23 07:22:33.219345+00:00","record_version_id":"6e093883246ceb8ef40bcbfd400c181b8d64fccb5d02cf046d9e1aff78ddc32d","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-c1fac4cbfde737f4f4ac02cdf15e6f5a9b5b676d","semester":"1262","observed_at":"2025-05-22 01:15:19.291664+00:00","record_version_id":"aebbe946265ff758a0fe3c17d8859165152b02b7156d38e2dd97cd06df6b8b3c","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-c6b62be45f8a13cba109ef2a7741b9cd9a6b8272","semester":"1262","observed_at":"2025-08-24 08:48:09.035112+00:00","record_version_id":"3d7d8c26b79cd7264c03a721d66d73149456136c4eb6fd0512e8272419935bb2","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-cc83f62cb6db61f39320916d819ad48ce55cd96d","semester":"1262","observed_at":"2025-05-22 00:45:35.735230+00:00","record_version_id":"9d0c1850564f52bd382cae9b22d293da625a1d9c489ffaf0ab6019d2d362fb0d","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d33818a01b6b4c5e2902e704da6e5b713742d4dc","semester":"1262","observed_at":"2025-10-13 10:46:24.251475+00:00","record_version_id":"2554c69da42a4d50d3d458d581252918f122ca99d5efca02ef2187d2266782f2","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d3c17db9832d3064916046caf891dd23f10b1bb9","semester":"1262","observed_at":"2025-08-26 11:30:42.288639+00:00","record_version_id":"bf758e7c4a18ac26e86d5e7869eac89771666c87da81bbc7701eb76ec843d443","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d4ee226dc44268e9b6767fb9f5f20343322f494b","semester":"1262","observed_at":"2025-06-15 01:52:23.911697+00:00","record_version_id":"dc126709db9eca63535f183ebb004fffb2c2d55317dfc1a5432f0b398fa580f9","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d8f9fc7f136e2033556d9d65bbdbdf33425dbdc9","semester":"1262","observed_at":"2025-05-28 16:48:12.400438+00:00","record_version_id":"b8c7f788d83f3e95ed04272bbb848af7649bae906b75138b1fc8a3857460e491","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dbbc9739c616c3846b2e796e00a36fa41225f7d8","semester":"1262","observed_at":"2025-06-01 17:47:19.325144+00:00","record_version_id":"6454c87c70e3b1263fa4d44ad021ebb0532b51e37f4ee207c0b9530c7afa9bf3","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dbe5f2d24b48c3177297a3d69c553cc9d1194bac","semester":"1262","observed_at":"2025-09-14 05:00:27.366070+00:00","record_version_id":"57219df28873f4b4bae918c0b70f056dd5e9da2950da8022142cf6ac7de56a18","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dd357dc2758e9e282c30988a527ce37de92593b9","semester":"1264","observed_at":"2025-10-19 01:39:41.951404+00:00","record_version_id":"b1a9cef1c8f5d8ea698218d1d06b3ea6a8ae0349984d3da7e5a92f077a3792a1","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-de74de559e409a3fe668685e28043b888d2e6841","semester":"1262","observed_at":"2025-06-27 07:38:50.882897+00:00","record_version_id":"0896db2912eafda80e29918cf8c7dcdbbee9377ae582f10a9f8c19fe2cd4e895","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-deca7188cf536ade3203cd88b52a45e92a059617","semester":"1262","observed_at":"2025-06-27 00:37:46.087071+00:00","record_version_id":"85d79b998f9306cace8498feae06d36a26c1497a5c0e8ccef7d41787c9dd01d9","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-df60fa9ac3931c5612b0fa641b7a6f5fbec86fab","semester":"1262","observed_at":"2025-05-24 06:36:37.554678+00:00","record_version_id":"58426c93da2950bd2cd97272c68280952d99b69503d4edb61ebfc551fa0a190e","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-e339da2d849aaf8bb4dceca07a84728af23cf755","semester":"1262","observed_at":"2025-07-23 08:49:22.748925+00:00","record_version_id":"2f070a67e1a85f47e58ea90416d69640e62227cefad244daf3c2140772db3216","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-e934b1784835f5d36ae9b7ef0992b11e72c39142","semester":"1262","observed_at":"2025-06-01 06:21:25.219533+00:00","record_version_id":"0b6c463834b73fed2726943e03f9ad19342804ac6541d598817a69d5a90982ae","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-ef471690c082448deebd2687eab84b0b78813c36","semester":"1262","observed_at":"2025-06-29 01:47:56.317645+00:00","record_version_id":"9a7fcc80a38cd85f6b5641e47b622bfe7d6d65b9e82465e990818a01611342bd","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-efc4e8e2cd7c3f68e059a308990c00c77c7611eb","semester":"1264","observed_at":"2025-10-16 05:48:13.935141+00:00","record_version_id":"a869132c6859529bba0e18126018a5b90d28419c2891115092ca4d9404ed6c59","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-f18b7749725097d41f69c60779ff38cf073b93b3","semester":"1262","observed_at":"2025-05-21 19:52:03.259353+00:00","record_version_id":"195756d663e8bcee4d77c45639e52fea68990eec18cce5122dc679dbae81bae8","course_id":"MATH 705","course_uid":"course_e48a9dd8b2c804c1634b4c32","catalog_version_id":"7d6df86d7f30a15b0fa2f77e63804061c059e884a5f9a8f28404dda71406e458","course_number":705,"subjects":["MATH"],"title":"MATHEMATICAL FLUID DYNAMICS","description":"Advanced introduction to fluid dynamics. Basic concepts; elementary viscous flow; Navier-Stokes equations. Elementary airfoil theory; boundary layers. Vortex motion. Waves. Very viscous flow. Compressible flows. Instabilities, bifurcations, turbulence. Requires working knowledge of multivariate calculus, differential equations and mechanics.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"}]