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METHODS OF APPLIED MATHEMATICS 1

MATH 703
과목 설명

Study of the linear algebraic structure underlying discrete equilibrium problems. Boundary value problems for continous equilibria: Sturm-Liouville equations, Laplace's equation, Poisson's equation, and the equations for Stokes flow. Contour integration and conformal mapping. Applications of dynamics leading to initial value problems for ODEs and PDEs. Green's functions for ODEs and introduction to asymptotic methods for ODEs, e.g. WKB analysis. Separation of variables and eigenfunction expansions for linear PDEs. Examples from physics and engineering throughout. Knowledge of undergraduate linear algebra, analysis and complex analysis is strongly recommended.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

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평점
3.74

-1.4% 과거 데이터 대비

수료율
96.77%

-1.77% 과거 데이터 대비

A 비율
70.97%

-10.49% 과거 데이터 대비

학급 규모
31

24.52% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

TECHNIQUES IN ORDINARY DIFFERENTIAL EQUATIONS

MATH 319

Review of linear differential equations; series solution of linear differential equations; boundary value problems; Laplace transforms; possibly numerical methods and two dimensional autonomous systems.

APPLIED MATHEMATICAL ANALYSIS 2: PARTIAL DIFFERENTIAL EQUATIONS

MATH 322

Sturm-Liouville theory; Fourier series, including mean convergence; initial and boundary value problems for linear second order partial differential equations, including separation of variables and eigenfunction expansions; fundamental solutions and Green's functions in multiple dimensions.

METHODS OF APPLIED MATHEMATICS-2

MATH 704

Derivation, nature and solution of canonical partial differential equations of applied mathematics. Conservation laws, advection, diffusion. First order PDEs, characteristics, shocks. Traffic flow, eikonal and Hamilton-Jacobi equations. Higher order PDEs: classification, Fourier analysis, well-posedness. Series solutions and integral transforms. Green's functions and distributions. Similarity solutions. Asymptotics of Fourier integrals. Laplace's method, stationary phase. Ship waves. Perturbation methods. Knowledge of undergraduate linear algebra, analysis and complex analysis is strongly recommended.

DYNAMIC SYSTEMS

ME 340

Mathematical modeling and analysis of dynamic systems with mechanical, thermal, and fluid elements. Topics: time domain solutions, analog computer simulation, linearization techniques, block diagram representation, numerical methods and frequency domain solutions. Students are assumed to have basic competence in particle and planar rigid body dynamics, matrix and vector algebra, and linear differential equations.

ANALYSIS OF PARTIAL DIFFERENTIAL EQUATIONS

MATH 619

A rigorous introduction to the theoretical underpinnings of the basic methods and techniques in the modern theory of PDEs. It is aimed at math majors, but will also be useful to some students in the sciences, engineering and economics who feel the need for a deeper understanding of the theory of PDEs. The emphasis is on the exposure to a number of different methods of solution of PDEs and their connection to physical phenomena modeled by the equations. The goals include both learning to solve some basic types of PDEs as well as to understand the motivation behind and inner workings of the techniques involved.