Math 319 (Fall 2013)

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.


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


Term Tests


  • 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)