Math 320 (Spring 2013)

This is the archived site for the Spring 2013 section of “Math 320: Differential Equations and Linear Algebra” as taught by Matthew D. Johnston at the University of Wisconsin – Madison.


  • Edwards and Penney, Differential Equations and Linear Algebra, 3rd Edition, Prentice-Hall


Term Tests


  • Week 1 (lecture notes) (Review, simple derivatives/integrals, definitions, classification of DEs)
  • Week 2 (lecture notes) (First-order DEs, acceleration/velocity models, slope fields, separable DEs, existence and uniqueness)
  • Week 3 (lecture notes) (First-order linear DEs, homogeneous DEs, Bernoulli DEs)
  • Week 4 (lecture notes) (Exact DEs, applications, population models, inflow/outflow models)
  • Week 5 (lecture notes) (Numerical methods, Euler’s method, Runge-Kutta method (supplemental note))
  • Week 6 (lecture notes) (Linear systems, Gaussian elimination, elementary row operations, row Reduction (supplemental note))
  • Week 7 (lecture notes: matrix operations and inverses) (Matrices and vectors, addition and subtraction, matrix multiplication, matrix inverses)
  • Week 8 (lecture notes) (Determinants, singular matrices, Cramer’s rule (note), the adjoint)
  • Week 9 (lecture notes) (Vector spaces, subspaces, linear independence)
  • Week 10 (lecture notes) (Basis for vector spaces, dimension and rank, row space, column space, null space)
  • Week 11 (lecture notes) (Eigenvalues and eigenvectors, characteristic equation, diagonalization)
  • Week 12 (lecture notes) (Secord-order linear DEs, existence and uniqueness, the Wronskian, homogeneous DEs with constant coefficients)
  • Week 13 (lecture notes) (Nonhomogeneous DEs with undetermined coefficients, method of undetermined coefficients, forced pendulum/spring, resonance)
  • Week 14 (lecture notes) (Homogeneous linear systems of DEs, reduction to first-order system, geometric approach)
  • Week 15 (lecture notes) (Solutions to linear systems, sinks, sources and saddles, phase portrait)