| Date | Notes |
| M 8/23 | Administriva. Introduction. δij, εijk, Gaussian integral. |
| W 8/25 |
Approximation of integrals, Stirling's approximation for n!
Chapter 1. Sequences, series. Tests of convergence. Preliminary test. Comparison test. |
| F 8/27 | Integral test. Euler's constant. Geometric series, ratio test. Alternating series. |
| M 8/30 | Ratio comparison test. Power series. Geometric series. Radius of convergence. |
| W 9/1 | Series for (1+x)p. Asymptotic behaviors, black-body radiation. |
| F 9/3 | Multiplying, dividing series. Pressure-driven (harmonic) oscillator. |
| M 9/6 | Labor Day (no class) |
| W 9/8 | Chapter 4. Multi-variable differential calculus. Partial derivatives, changing variables. |
| F 9/10 | Differentials, Legendre tranfsformation, cp − cv, changing variables in wave equation |
| M 9/13 | Implicit differentiation. Cyclic identity. Min/max with Lagrange multiplier. |
| W 9/15 | Chapter 5. Multi-variable integral calculus. Changing variables: Jacobian determinant |
| F 9/17 | Integrals along lines, curves (paths); surface areas |
| M 9/20 | Death star area (Example 1, p.272). Perimeter of an ellipse. |
| W 9/22 | Chapter 6. Vector derivatives and ∇:
gradient ∇φ,
divergence ∇·v, ,
curl ∇×v.
Product derivatives: ∇·(φv)
= (∇φ)·v + φ(∇·v)
etc.
See Table of vector identities involving ∇, p.339. |
| F 9/24 | Exam 1 (in class) |
| M 9/27 | Vector second derivatives, ∇²φ, ∇²v, ∇(∇·v). ∇×∇φ = 0, ∇·(∇×v) = 0. ∇²φ in cylindrical/spherical coordinates |
| W 9/29 | Fundamental theorem of calculus leads to Green's Theorem. |
| F 10/1 | Green's Theorem leads to Stokes's Theorem, Divergence Theorem |
| M 10/4 | Divergence theorem and Gauss's Law: point charges and the Dirac δ-function. |
| W 10/6 | Vector theorems and Maxwell's equations, equation of continuity, wave equation, gauge invariance |
| F 10/8 | Chapter 2. Complex numbers. Euler's relation: eiθ = cosθ + i sinθ |
| M 10/11 | Complex series. |
| W 10/13 | Multiple solutions to fractional powers, inverse trig functions, logarithms of complex numbers. Damped harmonic oscillator, LRC circuit. |
| F 10/15 | Homecoming (no class) |
| M 10/18 | Chapter 14: Functions of complex variable. Analytic functions, Cauchy-Riemann relations, harmonic functions. |
| W 10/20 | Cauchy's theorem, Cauchy's integral formula, Laurent series. |
| F 10/22 | Applications of Cauchy integral formula. Cauchy principal value. |
| F 10/29 | Exam 2 (in class) |
| M 11/1 | Square matrices: Identity, determinant, inverse, transpose |
| M 11/8 | Self-adjoint matrices have real eigenvalues, orthogonal eigenvectors. Unitary matrices, unitary transformations, eigenvector basis. detM = ∏λi. TrM = ∑λi. |
| W 11/10 | det(exp(M)) = exp(TrM). Modes of coupled springs. |
| F 11/12 | Functions as linear vector space, derivatives as linear operators. Schwarz inequality. Uncertainty principle. |
| M 11/15 | Periodic functions, einx as basis of orthogonal eigenvectors. |
| W 11/17 | Fourier cos/sin series. Triangle wave, square wave, overshoot. Convergence, Dirichlet conditions. |
| F 11/19 | Fourier exponential series. Square wave again. Parseval's theorem. ∑1/n² |
| M 11/22 | Arbitrary interval: cos/sin(nπx/L). Fourier transform. |
| F 11/26 | Thanksgiving (no class) | W 12/8 | Exam 3 (in class) |