# Math 332 syllabus

Differential Equations II

Course Description: Series solutions of second order linear equations. Numerical methods. Nonlinear differential equations and stability. Partial differential equations and Fourier series. Sturm-Liouville problems.
Prerequisites:  MA 227 Minimum Grade of C and MA 238 Minimum Grade of C

Suggested Text:   Fundamentals of Differential Equations and Boundary Value Problems, by R. Kent Nagle, Edward B. Saff and Arthur David Snider, 7th Edition, Pearson, 2018

Coverage: Chapter 8 (omit 8.8),  Chapter 9,  Chapter 5 (5.4-5.7), Chapter 10, Chapter 11 (11.1-11.3),  Chapter 12 (12.1 – 12.3)

Learning outcomes: Upon the successful completion of the course a student will:

Understand the linear algebraic (matrix) approach to solve linear systems of ODEs.
Find  the eigenvalues and eigenvectors of a matrix; write a system of differential equations in matrix form
Use the eigenvalue method to solve first-order linear systems
Find the fundamental matrix for a homogeneous linear system, to find matrix exponential solutions
Solve the nonhomogeneous first-order linear systems with constant coefficient matrix (the methods of undetermined coefficients and variation of parameters)
Understand phase-plane analysis techniques and stability of linear systems.
Sketch and interpret phase plane diagrams for systems of differential equations.
Classify critical points and identify the type of stability
Understand the power series method of solutions of linear differential equations
Use and manipulate Power series and Taylor series
Identify Ordinary points and regular singular points of an ODE
Apply the Frobenius' method
Understand Separation of Variables and Fourier methods for solving Partial Differential Equations
Find the Fourier series of periodic functions
Find the Fourier sine and cosine series for functions defined on a finite interval
Use the method of separation of variables to find solutions of certain partial differential equations
Find solutions of the heat equation, wave equation, and the Laplace equation subject to boundary conditions
Solve eigenvalue problems of Sturm-Liouville type and find eigenfunction expansions