Class Diary for PHZ 3113

  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, δij. cross product, εijk.
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 δ-function (Section 13.1.3). Properties of δ-function.
F 10/6 Homecoming (no class)
M 10/9 3D δ-function. 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. Cauchy-Riemann 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 self-adjoing 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 = δ-function, partial sum. numerical results. Parseval's theorem,
W 11/15 L → ∞, Fourier transform. 2π variations. Lorentzian, Gaussian examples. δ-function.
F 11/17 Fourier transform of "top hat". δ-function 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 Sturm-Liouville 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)