Differential Equations
First order DEs
IVPs, Direction Fields, Isoclines
Direction Fields, Autonomous DEs
Separable DEs, Exact DEs, Linear 1st order DEs
Numerical method: Euler (or Constant Slope)
Applications (Growth/Cooling/Circuits/Falling body)
Higher order DEs
IVPs/General solutions, Basic theory
Numerical methods for higher order DEs
Constant coefficient case: Undetermined Coefficients
Application: springs (free, damped, forced, pure resonance)
Application: Electrical Circuits
Inverse Laplace & Derivatives
1st Translation Thrm
Partial Fractions, completing the square
Unit Step Functions
2nd Translation Theorem
Derivative thrms, Solving DEs
Convolution theorem
Dirac Delta Function
Application: Lanchester's equations
Application: Electrical networks
PDEs
Separation of Variables
Heat Equation., Fourier's solution
Fourier Series
Convergence, Dirichlet's theorem
Fourier Sine Series, Fourier Cosine Series
Heat Eqn. Ends at Zero
Heat Eqn. Both Ends Insulated
