Physics

• Exponential Decay
• Resistors in Series and Parallel
• Variational Method
• Field Magnitude Relation
• Time Evolution Operator
• Bohr Atom Energies
• Plasma Frequency
• Infinite Square Well
• Energy-Momentum Tensor Conservation
• Newtonian Black Hole
• Rocket Equation
• Relativistic Energy
• Virial Theorem
• Kinetic Energy
• Energy-Mass Thought Experiment
• Center of Momentum Frame
• Massless Particles Travel at the Speed of Light
• Gyroscopic Precession

Mathematics

• Corollary of Divergence Theorem
• Vector Laplacian
• Differential Equation
• Random Walk in N Dimensions
• Power Series Expansions
• Variance Identity
• Curl Identity
• SU(2) Cayley-Klein Parameters
• Spherical Coordinates in N Dimensions
• Trace Identity
• Stirling Approximation
• Method of Integrating Factors
• Non-standard Analysis
• Dot Product Transpose Relation
• Unitary Transformations Preserve Norms
• Laplace Transforms
• Delta Function Representation
• Left and Right Matrix Inverses
• Extremum Change of Variables

Integration

• Leibniz Integral Theorem (Differentiation Under the Integral Sign)
• Integration Under the Integral Sign
• Differentiation With Respect to the Parameter
• Gaussian Integrals
• Logarithmic Integration
• Gamma Integrals
• Double Integration by Parts
• Bose-Einstein Integrals
• Sine Integral at Infinity

Physics Ideas

• Spherical Method of Images
• Complex Poynting Vector
• Multipole Expansion
• Outer Product Identity Operator
• Group Velocity
• EM waves are transverse
• EM waves travel at c
• Orbits are stable
• Uncertainty Principle
• Energy density in fields
• Larmor Formula
• Energy of a capacitor
• Poynting's Theorem (Griffiths)
• Equipartition Theorem (Reif)
• Pauli Exclusion Principle (Reif Pg 333)
• Liouville's Theorem (Marion & Thornton)
• Boltzmann Distribution
• Reconcile Lorentz Transformation Definitions

Mathematics Ideas

• Harmonic Addition Theorem
• DeMoivre's Theorem
• Divergence Theorem
• Stokes' Theorem
• Laplacian Solutions
• Component-based vector calculus
• When can you invert derivatives?
• Lagrange Multipliers
• Similar matrices have same trace
• Similarity transformation moves into exponent
• Linear Algebra Theorem 2.23
• Poisson Summation Formula