# Core Courses

#### Math 122: Complex Variables and Applications

Introduction to complex variables, analytic functions, contour integration and theory of residues. Mappings of the complex plane. Introduction to mathematical analysis.

Pre-requisites: Math 23 and Math 24

#### Math 125: Intermediate Differential Equations

This course introduces advanced solution techniques for ordinary differential equations (ODE) and elementary solution techniques for partial differential equations (PDE). Specific topics include higherorder linear ODE, power series methods, boundary value problems, Fourier series, Sturm-Liouville theory, Laplace transforms, Fourier transforms, and applications to one-dimensional PDE.

Pre-requisites: Math 23 and Math 24

#### Math 126: Partial Differential Equations

This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include Laplace's equation, heat equation, wave equation, application of Sturm-Liouville's theory, Green's functions, Bessel functions, Laplace transform, method of characteristics.

Pre-requisites: Math 125

#### 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

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

Phone: 209-228-4723

Phone: 209-228-4622

General Inquiries:
Phone: 209-228-4723
Fax: 209-228-6906

University of California, Merced
5200 N. Lake Road, SSB 310
Merced, CA 95343

The first new American research
university in the 21st century, with a
mission of research, teaching and service.

University of California, Merced