Math 121: Appied Mathematical Methods I: Fourier Analysis
and Boundary Value Problems
Introduction to Fourier series. Physical derivation of
canonical partial differential equations of mathematical
physics (heat, wave and Laplace's equation). Separation of
variables, Fourier series, Fourier integrals and general
eigenfunction expansions.
Pre-requisites: Math 23 and Math 24
Math 122: Appied Mathematical Methods II: Complex Variables
and Applications
Introduction to complex variables, contour integration and
theory of residues. Solving partial differential equations
by Fourier and Laplace transform methods. Introduction to
the theory of distributions and Green's functions.
Pre-requisites: Math 23 and Math 24
Math 131: Introduction to Numerical Analysis
Introduction to numerical methods with emphasis on algorithm
construction, analysis and implementation. Programming,
round-off error, solutions of equations in one variable,
interpolation and polynomial approximation, approximation
theory, direct solvers for linear systems, numerical
differentiation and integration, initial-value problems for
ordinary differential equations.
Pre-requisite: Math 24
Math 132: Numerical Solution of Differential Equations
A continuation of Math 131. Initial-value problems for
ordinary differential equations, iterative techniques for
solving linear systems, numerical solutions of nonlinear
systems of equations, boundary value problems for
ordinary-differential equations, numerical solutions to
partial-differential equations.
Pre-requisite: Math 131
Math 141: Linear Analysis I
Applied linear analysis of finite dimensional vector
spaces. Review of matrix algebra, vector spaces,
orthogonality, least-squares approximations, eigenvalue
problems, positive definite matrices, singular value
decomposition with applications in science and engineering.
Pre-requisite: Math 122, Co-requisite: Math 131
Math 142: Linear Analysis II
Applied linear analysis of infinite dimensional vector
spaces. Inner product spaces, operators, adjoint operators,
Fredholm alternative, spectral theory, Sturm-Liouville
operators, distributions and Green's functions with
applications in science and engineering.
Pre-requisite: Math 141