Applied Mathematics Lecture Notes

Peter J. Olver

Last Updated:    January 4, 2014



  1. Linear Algebraic Systems.
  2. Vector Spaces and Bases.
  3. Inner Products and Norms.
  4. Minimization and Least Squares Approximation.
  5. Orthogonality.
  6. Equilibrium.
  7. Linearity.
  8. Eigenvalues.
  9. Linear Dynamical Systems.
  10. Iteration of Linear Systems.
  11. Boundary Value Problems in One Dimension.
  12. Fourier Series.
  13. Fourier Analysis.
  14. Vibration and Diffusion in One-Dimensional Media.
  15. The Laplace Equation.
  16. Complex Analysis.
  17. Dynamics of Planar Media.
  18. Partial Differential Equations in Space.
  19. Nonlinear Systems.
  20. Nonlinear Ordinary Differential Equations.
  21. The Calculus of Variations.
  22. Nonlinear Partial Differential Equations.


    A.   Vector Calculus in Two Dimensions.
    B.   Vector Calculus in Three Dimensions.
    C.   Infinite Series.

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