Lecture transcripts
01 Transport Equation
02 Using Calculus
03 Method of Characteristics
04 Inviscid Burgers equation
See also the
animations on desmos
05 Method of Characteristics example
06 Inviscid Burgers equation
07 The wave equation, d'Alembert solution
see also the
Calculus derivation of the wave equation
08 Initial value problem for the wave equation
See
the desmos grapher
for animations of solutions
09 Boundary values for the wave equation
The desmos grapher has
an animation of the plucked string
10 generalized solutions to the Wave Equation (1)
11 Sequences of functions
Desmos graph of
uniform convergence without convergence of derivatives
Desmos graph of
Weierstrass’ nowhere differentiable function
12 Fourier solution to the wave equation (1)
13 Convergence of Fourier series
14 Inner Products and Fourier coefficients
15 The calculus of variations
16 The Euler—Lagrange equation
17 The minimal surface equation
18 Green’s Theorem
19 Convexity
20 Laplace’s Equation
21 Minimizing the Dirichlet integral
22 Distributions
23 Minimizing Dirichlet, using distributions
24 Random Walks, Brownian motion, and the Laplacian
Python script for the random walk simulation
25 The Maximum Principle
26 The heat equation
27 Backward heat equations