Below are some links to material I've written for students or myself. No claims of completeness or correctness is made.

• Problem Solving:
  • It's amazing how often students sit and stare at hard problems, waiting for inspiration, when there are in fact specific actions you can take to move forward. So here are some general notes I wrote for my calculus class, on problem solving (a distillation of Polya's ideas), and some specific strategies I've found useful over the years.
• Calculus Stuff:
  • Some notes on Taylor's Theorem for functions of several variables.
• DE/Matrix Algebra Stuff:
  • Some notes on simple Markov Models.
  • The Dirac Delta Function.
  • Some notes on basic Matrix Algebra.
• Probability/Stats:
  • Some notes on Continuous Random Variables.
• Analysis
  • Some notes on Compactness and Continuity in Metric Spaces
  • Some notes on Sequences in Euclidean n-space.
  • How to Complete a Metric Space.
  • A proof of the Existence-Uniqueness Theorem for ODE's.
  • When can you differentiate under an integral?
  • The Riesz Representation Theorem.
  • Some notes on functions from the complex numbers to a Banach Space.
  • Some notes on unbounded operators on a Hilbert Space.
  • Some notes on applications of functional analysis to Quantum Mechanics.
  • Some notes on Differential Forms.
  • Some notes on n-dimensional volume and change of coordinates.
  • Some notes on vector calculus.
• Mathematical Modelling
  • Notes on dimensional analysis and scaling.
  • Notes on conservation laws and the continuity equation in one-dimension. Applications to advection and traffic flow.
  • More on traffic flow and shocks.
  • Quick and dirty derivation of the wave equation.
  • Notes on autocatalytic waves in reaction-diffusion systems.
  • Notes on morphogenesis.
  • Notes on spatially distributed predator-prey models.
  • Notes on conservation laws in two dimensions, and the continuity equation in two dimensions. Also, some models one can derive using the continuity equation.
• Numerical Stuff
  • Finite differencing to estimate derivatives.
  • Quick intro to finite differencing to solve PDE's. And some more notes on differencing for PDE's.
• Optimization
  • Notes on one-dimensional optimization.
  • Notes on steepest descent optimization.
  • Notes on Newton's Method and improvements.
  • Notes on Conjugate Gradient methods.
  • Notes on Quasi-Newton methods.
  • Applications of optimization to data smoothing and filtering.
  • Methods for least-squares problems, and refinements.
  • BRIEF intro to the calculus of variations.
  • Introduction to penalty methods for constrained optimzation.
• PDE
  • The Wave Equation I, Wave Equation II, Wave Equation III, Wave Equation IV.
  • The Heat Equation derivation , Green's function, and maximum principle for the heat equation, and more stuff on the heat equation.
  • Notes on the Calculus of Variations and completeness of sines and cosines.
  • Notes on the Harmonic Functions and solvability of Laplace's Equation.
  • General remarks on PDE's and boundary conditions.
  • The reciprocity gap approach to inverse problem for finding internal defects.
• Number Theory
  • Notes on common factoring algorithms, e.g., Morrison-Brillhart and the Quadratic Sieve.