## Applied Mathematics Lecture Notes

Last Updated: January 4, 2014

### 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

- Linear Algebraic Systems.
- Vector Spaces and Bases.
- Inner Products and Norms.
- Minimization and Least Squares Approximation.
- Orthogonality.
- Equilibrium.
- Linearity.
- Eigenvalues.
- Linear Dynamical Systems.
- Iteration of Linear Systems.
- Boundary Value Problems in One Dimension.
- Fourier Series.
- Fourier Analysis.
- Vibration and Diffusion in One-Dimensional Media.
- The Laplace Equation.
- Complex Analysis.
- Dynamics of Planar Media.
- Partial Differential Equations in Space.
- Nonlinear Systems.
- Nonlinear Ordinary Differential Equations.
- The Calculus of Variations.
- Nonlinear Partial Differential Equations.

#### Appendices

A. Vector Calculus in Two Dimensions.

B. Vector Calculus in Three Dimensions.

C. Infinite Series.

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