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Chapter 4
Fourier series and PDEs

  3.4.4 Exercises
 3.5 Two dimensional systems and their vector fields
  3.5.1 Exercises
 3.6 Second order systems and applications
  3.6.1 Undamped mass-spring systems
  3.6.2 Examples
  3.6.3 Forced oscillations
  3.6.4 Exercises
 3.7 Multiple eigenvalues
  3.7.1 Geometric multiplicity
  3.7.2 Defective eigenvalues
  3.7.3 Exercises
 3.8 Matrix exponentials
  3.8.1 Definition
  3.8.2 Simple cases
  3.8.3 General matrices
  3.8.4 Fundamental matrix solutions
  3.8.5 Approximations
  3.8.6 Exercises
 3.9 Nonhomogeneous systems
  3.9.1 First order constant coefficient
  3.9.2 First order variable coefficient
  3.9.3 Second order constant coefficients
  3.9.4 Exercises