Math Resources

Less Formal

• Math3ma
  • Tensor Product
• Math ∩ Programming
  • Linear Algebra Primer
  • Inner Product Primer
  • Useful 3D Geometry Algorithms
  • Some notes on robustly calculating bending angles and their derivatives

Linear Algebra

• Interactive Linear Algebra, by Dan Margalit and Joseph Rabinoff

Solid Mechanics

• Continuum Mechanics
• Applied Mechanics of Solids

Programming/Computer Science

• Git - The Simple Guide
• Dynamic AABB Trees
• C++ STL Algorithm Cheat Sheet

Physical Simulation

• Physical Simulation from Geometric First Principles - Etienne Vouga
• Computational Physics using FEniCS (with a focus on EM)

Tools

• Inverse Symbolic Calculator - Useful for seeing if a number you're getting is related to some other kinds of constants/expressions
• Integer Sequences

Documents

• Useful Inequalities
• Matrix Algebra Cookbook
• Robust Calculation of Angles

Ideas

• Use complex numbers when doing simple 2D vector math. It simplifies rotations and scaling of vectors.

Mental Math and Simplifications

• $\phi \approx 1.618034$ and 1 mile $\approx$ 1.609344, so miles to km conversions can use the Fibonacci sequence. 130 km/hr $\approx$ 80 mph
• 1 lightnanosecond $\approx$ 1 foot
• $2^{10} \approx 10^3$ for making powers of 2 easier
• $1-x \leq e^{-x}$