This is the archived site for the Fall 2013 section of “Math 319: Techniques in Ordinary Differential Equations” as taught by Matthew D. Johnston at the University of Wisconsin – Madison.

**Textbook**

- Boyce and DiPrima,
*Elementary Differential Equations with Boundary Value Problems*, 9rd Edition

**Assignments**

- Assignment 1 (plus textbook problems)
- Assignment 2 (plus textbook problems)
- Assignment 3 (plus textbook problems)
- Assignment 4 (plus textbook problems)
- Assignment 5 (plus textbook problems)
- Assignment 6 (plus textbook problems)
- Assignment 7 (plus textbook problems)
- Assignment 8 (plus textbook problems)
- Assignment 9 (plus textbook problems)
- Assignment 10 (plus textbook problems)
- Assignment 11 (plus textbook problems)

**Term Tests**

- Term Test I (Section 001: Test – Solutions) (Section 002: Test – Solutions)
- Term Test II (Section 001: Test – Solutions) (Section 002: Test – Solutions)

**Lectures**

- Week 1 (lecture notes) (Review, definition of an ODE, solutions of ODEs, slope/direction fields)
- Week 2 (lecture notes) (First-order ODEs, existence and uniqueness, linear first-order ODEs)
- Week 3 (lecture notes) (Separable ODEs, substitution methods, power homogeneous ODEs, Bernoulli ODEs, exact ODEs)
- Week 4 (lecture notes) (Numerical methods, Euler’s formula, Runge-Kutta method, applications)
- Week 5 (lecture notes) (Second-order ODEs, homogeneous equations with constant coefficients)
- Week 6 (lecture notes) (Complex roots, repeated roots)
- Week 7 (lecture notes) (Nonhomogeneous second-order ODEs, method of undetermined coefficients, variation of parameters)
- Week 8 (lecture notes) (Applications, mechanical vibrations / pendulum, resonance)
- Week 9 (lecture notes) (Review of power series, radius of convergence, Solutions near ordinary points)
- Week 10 (lecture notes) (Laplace transforms, inverse Laplace transforms, Solutions of IVPs)
- Week 11 (lecture notes) (Discontinuous forcing functions, impulse/step functions)
- Week 12 (lecture notes) (Review of linear algebra, matrices and eigenvalues)
- Week 13 (lecture notes) (Conversion to first-order systems of DEs, phase plane)
- Week 14 (lecture notes) (First-order systems with constant coefficients, real/complex/repeated eigenvalues)
- Week 15 (lecture notes) (Fundamental matrix, nonhomogeneous linear systems)