Date 
Notes 
M 8/21 
Administriva, Introduction.
Rope around the earth.
Gaussian integral.

W 8/23 
Gamma function, Beta function.
Approximation of integrals, Stirling's approximation for n!

F 8/25 
Begin Chapter 4. Sequences and series.
Tests of convergence. Preliminary test. Comparison test.

M 8/28 
Sums of series. Integral test. Ratio test.
Geometric series. Logarithmic series. Power law power series.

W 8/30 
Alternating series.
Sample calculation.
Expansions and limits in physics: Blackbody radiation.

M 9/4 
Labor Day (no class)

W 9/6 
Chapter 5, partial derivatives.
Changing variables, expanding universe.
Useful theorems.
Thermodynamics and Maxwell relations.

F 9/8 
Hurricane Irma! (no class)

M 9/11 
Hurricane Irma!!! (no class)

W 9/13 
Hurricane Irma!! (no class)

F 9/15 
Implicit differentiation.
Max/min with constraints, Lagrange multipliers.

M 9/18 
Begin Chapter 6. Multiple integrals.
Change of variables, Jacobian, area in hyperbolic coordinates.
Integrals along curves.

W 9/20 
Lengths of curves and areas of surfaces.

F 9/22 
Exam 1 (in class) 
M 9/25 
Begin Chapter 7, Vectors.
Dot product, δ_{ij}.
cross product, ε_{ijk}.

W 9/27 
Chapter 10,
Vector derivatives, product rules.
Scalar, vector fields.
Vector derivatives, gradient, divergence, curl.
Second derivatives, Laplacian.

F 9/29 
Curl of a cross product.
Gradient, divergence, Laplacian in polar (cylindrical) coordinates.
Spherical coordinates.

M 10/2 
Chapter 11, integrals.
Green's Theorem.
Divergence Theorem, Stokes's Theorem.
Equation of continuity.

W 10/4 
Flux, divergence for point charge:
Dirac δfunction
(Section 13.1.3).
Properties of δfunction.

F 10/6 
Homecoming (no class) 
M 10/9 
3D δfunction.
Regularization of point charge.
Electromagnetism, charge conservation, electromagnetic waves.

W 10/11 
Chapter 3, Complex numbers. Euler's formula.

F 10/13 
Damped harmonic oscillator,
RLC circuit.
Chapter 24, Complex functions.
CauchyRiemann relations.

M 10/16 
Cauchy's theorem. Cauchy's formula.

W 10/18 
Applying Cauchy's formula:
ζ(2) as a contour integral.

F 10/20 
Complex contour integrals with branch cuts

M 10/23 
Matrix algebra, multiplication, determinant, inverse, transpose, trace.

F 10/27 
Exam 2 (in class) 
M 10/30 
Eigenvalues: vibrational modes of a molecule.

W 11/1 
Rotations. Projections.
Determinant, Trace invariants.

F 11/3 
Schwarz inequality, uncertainty principle.

M 11/6 
Eigenvalues and eigenvectors of selfadjoing linear differential operator,
L = i d/dθ.
Fourier series.

W 11/8 
Fourier series for square wave; convergence, overshoot.
numerical results.

F 11/10 
Veteran's Day (no class) 
M 11/13 
Integral of square wave = triangle wave.
numerical results.
Derivative of square wave =
δfunction, partial sum.
numerical results.
Parseval's theorem,

W 11/15 
L → ∞,
Fourier transform.
2π variations.
Lorentzian, Gaussian examples.
δfunction.

F 11/17 
Fourier transform of "top hat".
δfunction limits.
Convolution. Parseval's theorem.
Aside on Laplace transform, Mellin transform.

M 11/20 
Fourier transform solution of damped harmonic oscillator.
Fourier transform solution of Poisson's equation.

W–F 11/22–24 
Thanksgiving (no class) 
M 11/27 
SturmLiouville operator.
Bessel equation. Orthogonal polynomials, Hermite polynomials.

W 11/29 
Hermite polynomials.
Hermite series for sin(x),
Taylor series for sin(x)

F 12/1 
Partial differential equations,
Laplace/Poisson equation, wave equation, Schrö'dinger equation,
heat equation.
Separation of variables in Cartesian, spherical coordinates.

M 12/4 
Helmholtz equation, spherical waves, scattering,
Born approximation.

W 12/6 
Exam 3 (in class) 