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.
C or better in MA 227 and MA 238.
Differential Equations and Boundary Value Problems, 4th edition by C.H.
Edwards and D.E. Penney. Published by Prentice Hall.
Topics & Time Distribution as Follows—or as determined by instructor
- 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