Applied Mathematics Lecture Notes
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.
- Linear Algebraic Systems.
- Vector Spaces and Bases.
- Inner Products and Norms.
- Minimization and Least Squares Approximation.
- 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.