## Teaching

#### Math Methods in Physics I - PHYS 389

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

• Part 1: Taylor series

• Class 1   [ppt] [notes]
• Syllabus and overall overview. Euler formula. Taylor series.

• Class 2   [ppt] [notes]
• Properties of Series: convergence tests.

• Class 3   [notes]
• Properties of Series: binomial, long division.

• Class 4   [ppt] [notes]
• Accuracy of series approximation. Remainder theorem.

• Part 2: Complex numbers

• Class 5   [ppt] [notes]
• Roots of complex numbers, polar form, hyperbolic trigonometric functions.

• Class 6  [notes]
• Logarithm of complex numbers, complex powers.

• 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.

• Part 4: Interlude
• Class 19   [ppt] [notes]
• Partial derivatives.

• Class 20   [notes]
• Lagrange multipliers.

• Class 21   [ppt]  [notes]
• Path integral. Conservative fields. Gauss and Stokes theorems.

• 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.