# Math 332 syllabus

### Differential Equations II

Bulletin 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:

C or better in MA 227 and MA 238.

Textbook:

Differential Equations and Boundary Value Problems, 4th edition by C.H.
Edwards and D.E. Penney. Published by Prentice Hall.
ISBN #9780135143773

Topics & Time Distribution as Follows—or as determined by instructor

Coverage:

• Chapter 5 (omit 5.3)  - 4 weeks
• Chapter 6 (omit 6.3, 6.4 and 6.5) - 1.5 weeks
• Chapter 8 (omit 8.5 and 8.6) - 3 weeks
• Chapter 9 (omit 9.4) - 4 weeks
• Chapter 10 (omit 10.3-10.5) - 1.5 weeks

Note - time allotments are approximate and do not include exams.

MA 332 Differential Equations II Learning Objectives

• Understand the linear algebra approach to solve  first order linear systems
• Be able to 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
• Be able to find the fundamental matrix for a homogeneous linear system, to find matrix exponential solutions
• Be able to 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 critical points. Sketch and interpret phase plane diagrams for systems of differential equations.
• Understand the power series method of solution of differential equations
• Power and Taylor series
• Regular and ordinary singular points
• Frobenius' method
• Fourier series method
• Find the Fourier series of periodic functions
• Find the Fourier sine and cosine series for functions defined on an interval
• Apply the Fourier convergence theorem
• Use the method of separation of variables to find solutions to some 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

Last updated January 10, 2014