Lecture Notes and Tentative Schedule

These are lecture notes that I use. They are not a substitute for a good book or for going to class. But, if you miss one class they can work for you


Week 1: 8/28

Vectors, Tensors, Coordinate Systems:

  • Lecture 1: covariant, and covariance, rotations:
  • Lecture 2: dot product, cross-product, determinants, curl, Helmoltz theorem.
  • Lecture 3: Maxwell equations, electrostatics, stokes theorem and applications. Tensors.
Week 2: 9/4.

Vectors, Tensors, Coordinate Systems:

  • Lecture 4: General coordinate systems and metric:
  • Lecture 5: Orthogonal coordinate systems, General coordinate transformation
Week 3: 9/11

More Tensors:

  • Lecture 6: Covariant Differentiation, Div Grad Curl

Week 4: 9/18

Fourier Series and Transforms

  • Part 1: Hilbert Space, fourier series and transforms
  • Part 2: More about Fourier Transform

Week 5: 9/25

Complex Analysis:

  • Part 1 Cauchy Riemann Equations
  • Part 2 Integration and Cauchy formulas

Week 6: 10/2

More Complex Analysis:

  • Part 3 Example integrals and the radius of convergence
  • Part 4 Analytic continuation: the logarithm

Week 7: 10/9

Even More Complex Analysis:

  • Part 5 Example integrals with branch points and more complex continuations
  • Part 6 Principal value integrals
  • Part 7 Kramer's Kronig Relations
  • Part 8 The Gamma Function

Week 8: 10/16

Differential equations and Green functions

  • Part 1 Homogeneous and inhomogeneous equations and boundary conditions. General solution of 1st order equations.
  • Part 2 Green functions.
Week 9: 10/23

Differential equations and Green functions

  • Part 3 Solutions for constant coefficients and equidimensional equations
  • Part 4 Classification of singular points
Week 10: 10/30

Special functions and linear operators

  • Part 5 Differential operators and green therorem

Week 11: 11/6

Special functions and linear operators
Week 12: 11/13

Elementary Group Theory

Thanksgiving Week: 11/20

Monday class only

Week 13: 11/27

Elementary Group Theory

Week 14: 12/04

Elementary Group Theory

  • Part 3 Small oscillations
  • Part 4 Structure of Hamiltonian. Final answer on small oscillations.
  • Slides