Steps to Schrodinger's Equation

On my bucket list is to understanding Schrodinger's wave equation. I'm closer than even. Here are the steps and their components as I currently understand them.

1. The story of Ernst Schrodinger's equation
2. The basic point of the equation
3. Total energy (the Hamiltonian)
    --kinetic energy
    --momentum reformulation
    --potential energy
4. The Wave Equation
    --simple harmonic motion
    --taking derivatives
    --second derivatives
    --implicit differentiation
    --partial derivatives
    --derivatives of transcendental functions
5. The e form of the Wave Equation
    --cos x + i sin x = e to the ix
    --so psi equals e to the i times (kx-omega t)
6. Second derivative of psi function with respect to x
    --derivatives of e
    --Planck's constant and h bar
7. Time Independent Schrodinger Equation
8. Time Dependent Schrodinger Equation
9. The ket version
10. Dirac's relativistic version