| Differential Equations and Linear Algebra |
| Introduction |
| Lecture 01 - Overview of Differential Equations |
| Lecture 02 - The Calculus You Need |
| First Order Equations |
| Lecture 03 - Response to Exponential Input |
| Lecture 04 - Response to Oscillating Input |
| Lecture 05 - Solution for Any Input |
| Lecture 06 - Step Function and Delta Function |
| Lecture 07 - Response to Complex Exponential |
| Lecture 08 - Integrating Factor for Constant Rate |
| Lecture 09 - Integrating Factor for a Varying Rate |
| Lecture 10 - The Logistic Equation |
| Lecture 11 - The Stability and Instability of Steady States |
| Lecture 12 - Separable Equations |
| Second Order Equations |
| Lecture 13 - Second Order Equations |
| Lecture 14 - Forced Harmonic Motion |
| Lecture 15 - Unforced Damped Motion |
| Lecture 16 - Impulse Response and Step Response |
| Lecture 17 - Exponential Response ? Possible Resonance |
| Lecture 18 - Second Order Equations with Damping |
| Lecture 19 - Electrical Networks: Voltages and Currents |
| Lecture 20 - Method of Undetermined Coefficients |
| Lecture 21 - An Example of Undetermined Coefficients |
| Lecture 22 - Variation of Parameters |
| Lecture 23 - Laplace Transform: First Order Equation |
| Lecture 24 - Laplace Transform: Second Order Equation |
| Lecture 25 - Laplace Transforms and Convolution |
| Graphical and Numerical Methods |
| Lecture 26 - Pictures of Solutions |
| Lecture 27 - Phase Plane Pictures: Source, Sink, Saddle |
| Lecture 28 - Phase Plane Pictures: Spirals and Centers |
| Lecture 29 - Two First Order Equations: Stability |
| Lecture 30 - Linearization at Critical Points |
| Lecture 31 - Linearization of Two Nonlinear Equations |
| Lecture 32 - Eigenvalues and Stability: 2 by 2 Matrix, A |
| Lecture 33 - The Tumbling Box in 3-D |
| Vector Spaces and Subspaces |
| Lecture 34 - The Column Space of a Matrix |
| Lecture 35 - Independence, Basis, and Dimension |
| Lecture 36 - The Big Picture of Linear Algebra |
| Lecture 37 - Graphs |
| Lecture 38 - Incidence Matrices of Graphs |
| Eigenvalues and Eigenvectors |
| Lecture 39 - Eigenvalues and Eigenvectors |
| Lecture 40 - Diagonalizing a Matrix |
| Lecture 41 - Powers of Matrices and Markov Matrices |
| Lecture 42 - Solving Linear Systems |
| Lecture 43 - The Matrix Exponential |
| Lecture 44 - Similar Matrices |
| Lecture 45 - Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors |
| Lecture 46 - Second Order Systems |
| Applied Mathematics and ATA |
| Lecture 47 - Positive Definite Matrices |
| Lecture 48 - Singular Value Decomposition (the SVD) |
| Lecture 49 - Boundary Conditions Replace Initial Conditions |
| Lecture 50 - Laplace Equation |
| Fourier and Laplace Transforms |
| Lecture 51 - Fourier Series |
| Lecture 52 - Examples of Fourier Series |
| Lecture 53 - Fourier Series Solution of Laplace's Equation |
| Lecture 54 - Heat Equation |
| Lecture 55 - Wave Equation |