| I. First-order Differential Equations |
| 1 |
Introduction
Separable Equations
Direction Fields |
(PDF) |
| 2 |
Isoclines
Models |
(PDF) |
| 3 |
Linear Equations |
(PDF) |
| 4 |
Autonomous Equations
The Phase Line |
(PDF) |
| 5 |
Complex Numbers
Complex Exponential |
(PDF) |
| 6 |
Sinusoidal Functions |
(PDF) |
| 7 |
Sinusoidal System Response |
(PDF) |
| II. Second-order Linear Equations |
| 9 |
Solutions of Spring-mass-dashpot Models |
(PDF) |
| 10 |
Superposition
Initial Conditions |
(PDF) |
| 11 |
Damping Conditions
Inhomogeneous Equations |
(PDF) |
| 12 |
Exponential Signals |
(PDF) |
| 13 |
Operator Notation and Undetermined Coefficients |
(PDF) |
| 14 |
Frequency Response |
(PDF) |
| 15 |
Resonance |
(PDF) |
| 16 |
Review |
(PDF) |
| III. Delta Functions and Convolution |
| 18 |
Step and Delta Functions |
(PDF) |
| 19 |
Impulse Response and Convolution |
(PDF) |
| 20 |
From Convolution to the Laplace Transform |
(PDF) |
| IV. The Laplace Transform |
| 21 |
Laplace Transform: Basic Properties |
(PDF) |
| 22 |
Application to ODEs
Partial Fractions |
(PDF) |
| 23 |
Completing the Square
Transforms of Delta and Time Translated Functions |
(PDF) |
| 24 |
Convolution and Laplace Transform
The Pole Diagram |
(PDF) |
| 25 |
Numerical Methods |
(PDF) |
| V. Fourier Series |
| 26 |
Fourier Series |
(PDF) |
| 27 |
Differentiating and Integrating |
(PDF) |
| 28 |
General Period |
(PDF) |
| 29 |
Periodic Solutions |
(PDF) |
| 30 |
Review: Fourier, Euler, Laplace |
|
| VI. First-order Systems |
| 32 |
Linear Systems and Matrices |
(PDF) |
| 33 |
Eigenvalues
Eigenvectors |
(PDF) |
| 34 |
Complex or Repeated Eigenvalues |
(PDF) |
| 35 |
Qualitative Behavior of Linear Systems |
(PDF) |
| 36 |
Normal Modes and the Matrix Exponential |
(PDF) |
| 37 |
Inhomogeneous Equations |
(PDF) |
| 38 |
Nonlinear Systems
The Phase Plane |
(PDF) |
| 39 |
Examples of Nonlinear Systems |
(PDF) |