World of Knowledge

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Math

Three simple boundary value problems demonstrating some of the types of solutions
Solution to a heat equation scenario with animations (Maple worksheet)
Solving a regular Sturm-Liouville problem and using it to approximate a function
Eigensolutions to a regular Sturm-Liouville problem
Using an orthogonal series to approximate a function

A 1st-order nonhomogenous ODE solved by using an integrating factor
A story problem involving a lake with changing volume and salt concentrations
An inexact ODE solved two different ways
Variation of parameters
A nonlinear 2nd-order ODE
A nonlinear ODE that's missing an independent variable
A tricky 2nd-order-linear-homogeneous-ODE
A linear ODE solved two ways: using a Laplace transform and using the method of Undetermined Coenfficients
A tricky nonlinear IVP
Using power series to solve an ODE
Using the Residue Theorem to solve an IVP
Finding a one-parameter family of solutions
Finding a one-parameter family of solutions and plotting the direction field (Maple worksheet)
Solving a system of differential equations using eigenvalues and eigenvectors

In which it is determined whether a sequence converges
In which the flux of a vector field over a closed surface is computed directly
The same flux problem as above except that the divergence theorem is used instead
Find the volume of a solid with given base and cross sections.
Find the arc length of a parametric curve between two points
In which a line integral is used to compute the mass of a rod whose density varies along its length.
Lagrange multipliers
Using Green's Theorem to calculate a line integral about a closed region
Convergence of power series

Talking 'bout fictitious forces
A story problem involving projectile motion
Center of mass
Circular motion
Work and energy in a ramp
How much does the rotation of the Earth affect your weight?
Physical pendulum
The probability density function (and more) of a particle undergoing simple harmonic motion

What is the probability that a particle in the ground state of the quantum harmonic oscillator will be observed outside the classically allowed region?
Scattering from a step potential
The spin-$\frac{3}{2}$ system
Expanding an observable in terms of eigenvalues and projection operators
The delta function potential
How an external magnetic field affects a spin-1/2 particle
Doubling the width of an infinite square well
Decomposing a wavefunction into eigenfunctions
Animating the time evolution of a quantum superposition

Chapter 1: Introduction, units, dimensional analysis, significant digits, and scientific notation
Chapter 2: Motion in one dimension, constant acceleration
Chapter 3: Motion in two or three dimensions, vectors, relative velocity, circular motion
Chapters 4/5: Forces and Newton's laws
Chapters 6/7: Work, energy, and its conservation
Chapter 8: Impulse, momentum and its conservation, center of mass
Chapter 9: Rotational motion, moment of inertia, torque
Chapter 12: Universal gravitation, escape velocity
Chapter 29: Electromagnetic induction, Faraday's law, displacement current