Math 253, 2002 spring syllabus

The following is a schedule from the spring semester, 2001/2:

Week 1 (11-15 Feb.)
Classification of differential equations, Direction fields,
2.1 Linear equations with Variable Coefficients

Week 2 (18-21 Feb.)
2.2 Separable equations,
2.3 Modeling with first order equations

Week 3 (26 Feb.-01 March)
2.4 Differences between linear and nonlinear equations,
2.6 Exact equations and integrating factors

Week 4 (04-08 March)
2.7 Numerical approximations: Euler's method,
2.8 The existence and uniqueness theorem,
3.1 Homogeneous equations with constant coefficients,
3.2 Fundamental solutions of linear homogeneous equations

Week 5 (11-15 March)
3.3 Linear independence and the Wronskian, Complex numbers,
3.4 Complex roots and the characteristic equation,
3.5 Repeated roots; reduction of order

Week 6 (18-22 March)
3.6 Nonhomogeneous equations; method of undetermined coefficients,
3.7 Variation of parameters, Modelling of second order mechanical systems

Week 7 (25-29 March)
4.1 General theory of nth order linear equations,
4.2 Homogeneous equations with constant coefficients,
4.3 The method of undetermined coefficients

Week 8 (01-05 April)
Convolution and system response,
6.1 Definition of the Laplace transform,
6.2 Solution of initial value problems

Week 9 (08-12 April) 6.3 Step functions,
6.4 Differential equations with discontinuous forcing functions,
6.5 Impulse functions

Week 10 (15-19 April)
6.6 The convolution integral, Linear algebra

Week 11 (22-26 April)
Linear Algebra

Week 12 (29 April-3 May)
7.5 Homogeneous linear systems with constant coefficients,
7.6 Complex eigenvalues,
7.7 Repeated eigenvalues

Week 13 (6-10 May)
9.1 The phase plane: linear systems,
9.2 Autonomous systems and stability,
9.3 Almost linear systems,
5.1 Review of Power series

Week 14 (13-17 May)
5.2 Series Solution near an ordinary point, Part I,
5.3 Series Solution near an ordinary point, Part II,
5.4 Regular singular points

Week 15 (20-24 May)
5.5 Euler Equations,
5.6 Series Solution near a regular singular point,Part I,
5.7 Series Solution near a regular singular point, Part II