Department of Mathematics - RHIT
last posted to site: 08/19/10
Topics Outline for MA222 - Differential Equations and Matrix Algebra II - 2010-11
Text and Text Materials
Text: Differential Equations with Boundary Value Problems, second edition, by Polking, Bogess, and
Approximate Timing and Pace
There should be 2 or 3 tests, perhaps a final review day or two.
It may be advantageous to teach Laplace transforms first. However, no engineering courses have MA222
as corequisite for course require to be taken at the same time as MA222. Therefore, there are no requirements
to teach Laplace transforms first.
Optional topics in italics.
||5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7
|Systems of differential equations
3.5 weeks total
|8.1, 8.2, 8.3, 8.4, 8.5
9.1, 9.2, 9.3, 9.5, 9.9
10.1, 10.2, 10.5, 10.6, 10.8
||6.1, 11.1, 11.2, 12.1, 12.2, 12.3
|Tests and flex/review
Text Topics - listed in the approximate book order - optional topics in italics.
Laplace Transform Methods - about 3 weeks
Chapter 5: The Laplace Transform
- 5.1 - The Definition of the Laplace Transform.
- 5.2 - Basic Properties of the Laplace Transform
- 5.3 - The Inverse Laplace Transform
- 5.4 - Using the Laplace Transform to Solve Differential Equations.
- 5.5 - Discontinuous Forcing Terms.
- 5.6 - The Delta Function.
- 5.7 - Convolutions
Systems of differential equations - about 3.5 weeks
Chapter 8: An Introduction to Systems (about 1 week)
- 8.1 - Definitions and Examples.
- 8.2 - Geometric Interpretation of Solutions.
- 8.3 - Qualitative Analysis.
- 8.4 - Linear Systems.
- 8.5 - Properties of Linear Systems.
Chapter 9: Linear Systems with Constant Coefficients (about
- 9.1 - Overview of the Technique. Planar Systems. (mostly review of eigenvalues and eigenvectors)
- 9.2 - Planar Systems
- 9.3 - Phase Plane Portraits
- 9.5 - Higher Dimensional Systems (deficient matrices optional)
- 9.9 - Inhomogeneous Linear Systems (undetermined coefficients only)
Chapter 10: Nonlinear Systems (about 1 week)
- 10.1 - The Linearization of a Nonlinear System
(in classification just the characterization: stable, asymptotically stable,
- 10.2 - Long-Term Behavior of Solutions
- 10.5 - Conserved Quantities
- 10.6 - Nonlinear Mechanics (lightly, may need a small amount of material from 10.5)
- 10.8 - Predator - Prey Systems (simple examples)
Approximation - about 2.5 weeks
Chapter 6: Numerical Methods
- 6.1 - Euler’s Method. (there is one small section on systems)
Chapter 11: Series Solutions to Differential Equations
- 11.1 - Review of Power Series.
- 11.2 - Series Solutions Near Ordinary Points - First and second order equations.
Chapter 12: Fourier Series
- 12.1 - Computation of Fourier Series.
- 12.2 - Convergence of Fourier Series.
- 12.3 - Fourier Cosine and Sine Series.
- Optional topic -Fourier series for solving second order systems with a periodic forcing term
- not in text