Applied Mathematics Lecture Notes

Peter J. Olver

Last Updated:    December 14, 2012

Note: The first 11 chapters, including the exercises, are now published as a self-contained textbook, Applied Linear Algebra, coauthored with Chehrzad Shakiban. By popular demand, the later chapters are again available on-line. Thanks to everyone for their encouraging feedback and comments.

Click here for Lecture Notes on Partial Differential Equations.

Click here for Lecture Notes on Numerical Analysis.

Chapters

  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.

References

Appendices