Menu:

Teaching

Math Methods in Physics I - PHYS 389

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

Syllabus

Download course material (zip file).

  • 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.