Boundary Value Problems
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Three simple boundary value problems demonstrating some of the types of solutions
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Solution to a heat equation scenario with animations (Maple worksheet)
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Solving a regular Sturm-Liouville problem and using it to approximate a function
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Eigensolutions to a regular Sturm-Liouville problem
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Using an orthogonal series to approximate a function
Differential Equations
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A nonlinear ODE that's missing an independent variable
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A tricky 2nd-order-linear-homogeneous-ODE
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Variation of parameters
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A nonlinear 2nd-order ODE
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An inexact ODE solved two different ways
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A linear ODE solved two ways: using a Laplace transform and using the method of Undetermined Coefficients
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A 1st-order nonhomogenous ODE solved by using an integrating factor
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A story problem involving a lake with changing volume and salt concentrations
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A tricky nonlinear IVP
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Finding a one-parameter family of solutions
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Using the Residue Theorem to solve an IVP
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Finding a one-parameter family of solutions and plotting the direction field (Maple worksheet)
Statistics
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Calculating a p-score
Linear Algebra
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Decompose a polynomial into parts within and without a subspace
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In which it is determined whether a sequence converges
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In which the flux of a vector field over a closed surface is computed directly
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The same flux problem as above except that the divergence theorem is used instead
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Find the volume of a solid with given base and cross sections.
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Find the arc length of a parametric curve between two points
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In which a line integral is used to compute the mass of a rod whose density varies along its length.
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Using Green's Theorem to calculate a line integral about a closed region
Mechanics
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Talking 'bout fictitious forces
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A story problem involving projectile motion
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Center of mass
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Circular motion
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Work and energy in a ramp
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How much does the rotation of the Earth affect your weight?
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Physical pendulum
Electricity and Magnetism
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Rutherford scattering
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A couple of circuits with resistors solved using Kirchoff's rules
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An RC circuit solved using differential equations
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Power in an electric circuit
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A solenoid
More
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How to solve lens problems without memorizing a lot of equations
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Ray tracing
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A thermodynamics problem
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The famous train/tunnel "paradox" from relativity
Notes
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Chapter 1: Introduction, units, dimensional analysis, significant digits, and scientific notation
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Chapter 2: Motion in one dimension, constant acceleration
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Chapter 3: Motion in two or three dimensions, vectors, relative velocity, circular motion
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Chapters 4/5: Forces, Newton's laws,
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Chapters 6/7: Work, energy, and its conservation
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Chapter 8: Impulse, momentum and its conservation, center of mass
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Chapter 9: Rotational motion, moment of inertia, torque
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Chapter 12: Universal gravitation, escape velocity
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Chapter 29: Electromagnetic induction, Faraday's law, displacement current
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A flowchart for determing the pH of acid/base solution
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Can you figure out the concetration of a solution from its pH?
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Solution to an AP free response question involving an acid/base solution
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An illustrated chart showing molecular geometries with examples