Algebra

• Rotate a conic section to eliminate the $xy$ terms
• Find the point of tangency between a circle and line without using calculus
• Solve optimization problems without using calculus
• Weighted averages
• Find the set of vectors that are a certain distance from a certain plane

Geometry

• Central Angle Theorem (proof)
• A proof involving triangles
• A proof involving a parallelogram
• A table showing some points of concurrency in triangles and their properties

Calculus

• 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

Calculus notes

• 1.1: A Preview of Calculus
• 1.2: Finding Limits Graphically and Numerically
• 1.3: Evaluating Limits Analytically
• 1.4: Continuity
• 1.5: Infinite Limits
• 2.1: The Derivative and the Tangent Line Problem
• 2.2: Basic Differentiation Rules and Rates of Change
• 2.3: Product and Quotient Rules and Higher-Order Derivatives
• 2.5-2.6: Implicit Differentiation and Related Rates
  
• 3.1-3.4: Extrema, Concavity, and the Mean Value Theorem
  
• 3.5-3.9: Infinite limits, Curve Sketching, Optimization, Newton's Method, Differentials
  
• 4.1-4.2: Antiderivatives and Area Integrals
  
• 4.3-4.6: Riemann Sums and the Fundamental Theorem of Calculus
  
• 5.1-5.3: The Natural Logarithm and Inverse Functions
  
• 5.4-5.8: Exponential Functions, Inverse Trig Functions, and Hyperbolic Functions
  

Differential Equations

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

Boundary Value Problems

• 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