325 Differential Equations    Fall 1996

Dennis Snow

TEXT:  Boyce & DiPrima, Elementary Differential Equations and Boundary
Value Problems, Fifth Edition

Syllabus

4. Higher Order Linear Equations
(4 classes:)
4.1 n-th order linear equations
4.2 Homogeneous equations with constant coefficients
4.3 Undetermined coefficients 

8. Numerical Methods
(3 classes:)
8.1 Euler method
8.2 Errors 
8.4 Runge-Kutta 

6. The Laplace Transform
(8 classes:)
6.1 Definition of Laplace transform
6.2 Solution of initial value problems 
6.3 Step functions
6.4 Discontinuous forcing functions 
6.5 Impulse functions 
6.6 Convolution integral 

7. Systems of First Order Linear Equations
(12 classes:)
7.1 Intro to systems of 1st order equations 
7.2 Matrices 
7.3 Linear systems/independence, eigenvalues/vectors
7.4 Basic Theory of 1st order systems
7.5 Homogeneous systems, constant coefficients
7.6 Complex eigenvalues  
7.7 Repeated eigenvalues 
7.8 Fundamental matrices 
7.9 Nonhomogeneous linear systems (variation of parameters)

9. Nonlinear Differential Equations and Stability
(7 classes:)
9.1 Autonomous systems 
9.2 Phase plane: linear systems, Mma
9.3 Almost linear systems, pendulum, Mma
9.4 Competing Species, Mma
9.5 Predator-Prey

10. Partial Differential Equations and Fourier Series
(8 classes:)
10.1 Separation of variables, heat conduction
10.1 Separation of variables, heat conduction\cr
10.2--4 Fourier series (summary) 
10.5 Heat equation: non-homogeneous boundary conditions
10.6 Wave equation