TOPICS IN MULTI-VARIABLE CALCULUS AND LINEAR ALGEBRA

MATH 320

An introduction to linear algebra and differential equations with emphasis on the relationship between the theory of linear algebra and analytical and numerical techniques for solving differential equations. Linear algebra topics include linear systems, matrices and their algebra, vector spaces and linear transformations, eigenvalues and eigenvectors. Topics from differential equations include first order ODE, homogeneous and nonhomogeneous linear systems, and numerical methods.

MATH 234

Introduction to calculus of functions of several variables; calculus on parameterized curves, derivatives of functions of several variables, multiple integrals, vector calculus.

MATH 321

Vector analysis: algebra and geometry of vectors, index notation, 3D rotations, Euler angles; vector differential and integral calculus, theorems of Green, Gauss, and Stokes; grad, div, curl, and Laplacian in cylindrical and spherical coordinates; Complex analysis: analytic functions, Cauchy-Riemann equations, conformal mapping, complex integrals, residue theorem.

MATH 376

Topics in multi-variable calculus and introduction to differential equations.

MATH 621

Integration in Euclidean spaces, change of variables, multilinear algebra, vector fields and differential forms, manifolds and tangent spaces, integration on manifolds, Stokes theorem. Classical vector analysis. Cauchy integral theorem.