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