Story

If you can solve the hardest problem, then everything else is easy.

Key ideas:

1. Calculus of Variations
   1. Functional Variation and Derivative
   2. Noether’s Theorem
   3. Lagrange Multiplier
2. Ordinary Differential Equations
   1. Banach Space vs. Hilbert Space
   2. Distributional Derivative
   3. Wronskian
   4. Reduction of Order
   5. Completeness
   6. Self-Adjoint Operator (Lagrange’s Identity)
   7. Green’s Function
   8. Damped Harmonic Oscillator
3. Partial Differential Equations
   1. Wave Equation
   2. Heat Equation
   3. Potential Theory and Vector Potential Theory
4. Physics of Real Waves
   1. 1D Sound Wave
   2. Ocean Wave
   3. Berger’s Shock
5. Special Functions
   1. Generating Function and Normalization
   2. Bessel’s Equation
6. Integral Equations
   1. Classification
   2. Integral Transform