Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials.

1. Integral Curves
2. Euler's Method for y'=f(x,y)
3. Solving First-order Linear ODE's
4. Bernouilli and Homogeneous ODE's
5. First-order Autonomous ODE's
6. Complex Numbers and Exponentials
7. First-order Linear with Constant Coefficients
8. Applications
9. Solving Second-order Linear ODEs
10. Undamped and Damped Oscillations
11. Theory of General 2nd-Order ODEs
12. Theory for Inhomogeneous ODE's
13. Finding Sto Inhomogeneous ODE's
14. Resonance
15. Introduction to Fourier Series
16. Even and Odd Functions
17. Solutions via Fourier Series
18. Intro to the Laplace Transform
19. Using the Laplace Transform
20. Convolution Formula
21. Using the Laplace Transform
22. Dirac Delta Function
23. First-order Systems of ODE's
24. Homogeneous Linear Systems
25. Complex Eigenvalues
26. Sketching Linear Systems
27. Matrix Methods for Systems
28. Matrix Exponentials
29. Decoupling Linear System
30. Non-linear Autonomous Systems
31. Limit Cycles
32. Relations Between Systems

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

The original name of this course is: 18.03 Differential Equations.