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The table below is a rough guideline for the content of course lectures. Professors may reorder their lectures as necessary/desired. Section and page numbers below are from the textbook, Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, 9^th ed., 2010.

• Week 1 (July 2-6)
  • Introduction. Direction fields.
  • §2.1: Linear equations with variable coefficients.
  • §2.2: Separable equations, homogeneous equations.
  • §2.3: Modeling with first order equations (parts of).
  • §2.4: Differences between linear and nonlinear equations.
  • §2.6: Exact equations and integrating factors.
  • §7.1: Introduction to linear systems.
• Week 2 (July 9-13)
  • §7.2: Review of matrices.
  • §7.3: Systems of linear algebraic equations: Linear independence, eigenvalues, eigenvectors.
  • §7.4: Basic theory of systems of first order linear equations.
  • §7.5: Homogeneous linear systems with constant coefficients.
  • §7.6: Complex eigenvalues.
• Week 3 (July 16-20)
  • §7.7: Fundamental matrices.
  • §7.8: Repeated eigenvalues, Jordan form of a matrix.
  • §7.9: Nonhomogeneous linear systems (Variation of parameters).
  • §4.1: General theory of n^th order linear equations.
  • §4.2: Homogeneous equations with constant coefficients.
  • §3.2: Fundamental solutions of linear homogeneous equations.
• Week 4 (July 23-27)
  • §3.3: Linear independence and the Wronskian.
  • §3.4: Complex roots and the characteristic equation.
  • §3.5: Repeated roots; reduction of order.
  • §3.6: Nonhomogeneous equations; method of undetermined coeff.
  • §4.3: The method of undetermined coefficients.
  • §3.7: Variation of parameters.
  • §3.8: Mechanical and electrical vibrations.
  • §3.9: Forced vibrations.
• Week 5 (July 30-August 3)
  • §6.1: Definition of the Laplace transform.
  • §6.2: Solution of initial value problems.
  • §6.3: Step functions.
  • §6.4: Differential equations with discontinuous forcing functions.
  • §6.5: Impulse functions.
  • §6.6: The convolution integral.
• Week 6 (August 6-10)
  • §10.1: Two point boundary value problems.
  • §10.2: Fourier series.
  • §10.3: The Fourier convergence theorem.
  • §10.4: Even and odd functions.
  • §10.5: Separation of variables, heat conduction in a rod.