New Mexico State University

Department of Astronomy

PO Box 30001, MSC 4500 Las Cruces, NM 88003

wlyra - nospam - nmsu.edu

+1 575-646-1400

Lectures for the course *Math Methods in Physics I*, an undergraduate course at CSUN.

Download course material (zip file).

**Part 1: Taylor series****Part 2: Complex numbers****Part 3: Linear Algebra**- Class 7 [notes]
- Recap of matrix properties. Row reduction. Kramer rule. Determinants. Levi-Civita symbol. Kronecker delta.

- Class 8
- Solution of homework list (TA Michael Artinian)

- Class 9 [ppt] [notes]
- Rotation, index notation.

- Class 10 [notes]
- 3D rotation, functions of matrices, linear operators.

- Class 11
- Eigenvalue and eigenvector. TA Vincent Carpenter.

- Class 12
- Eigenvalue and eigenvector. TA Vincent Carpenter.

- Class 13 [ppt] [notes]
- Eigenvalue and eigenvector. Matrices in complex plane.

- Class 14
- Midterm.

- Class 15
- Solution of midterm.

- Class 16 [ppt] [notes]
- Projections. Least squares.

- Class 17 [ppt] [notes]
- Eigendecomposition. Special matrices.

- Class 18 [ppt] [notes]
- Fibonacci numbers. Golden ratio.

- Class 7 [notes]
**Part 4: Interlude****Part 5: Fourier series and Fourier transforms**- Class 22 [ppt] [notes]
- Fourier series.

- Class 23 [notes]
- Dirichilet conditions.

- Class 24 [ppt] [notes]
- Even/odd functions. Gibbs phenomenon.

- Class 25 [ppt] [notes]
- Fourier transform.

- Class 26 [ppt] [notes]
- Linearization of nonlinear problems: Kepler problem; epicycle solution.

- Class 27 [notes]
- Parseval theorem.

- Class 28 [notes]
- Wave equation, harmonic oscillator, Poisson equation.

- Class 22 [ppt] [notes]