Applied Mathematics Lecture Notes

Peter J. Olver

Note:

• The first 11 chapters, including the exercises, are now published as a self-contained textbook, Applied Linear Algebra, coauthored with Chehrzad Shakiban.
• Most of chapters 11-15, 17, 18, and 22, including the exercises, are now incorporated in my new textbook, Introduction to Partial Differential Equations.
• The remaining chapters, appendices, and additional material are still available online in the author's various lecture notes.
• Thanks to everyone for their encouraging feedback and comments!

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.

Appendices

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