| I. First-order Differential Equations |
| 1 |
Introduction
Natural Growth and Decay
Review of Logarithm |
(PDF) |
No Solutions for R1 |
| 2 |
First-order Equations: Language and Examples |
(PDF) |
(PDF) |
| 3 |
First-order Linear Equations |
(PDF) |
(PDF) |
| 4 |
Autonomous Equations |
(PDF) |
(PDF) |
| 5 |
Review (PDF)
New Topics: Complex Numbers, Complex Exponentials, Sinusoidal Functions, and How they Appear in First-order Linear Constant Coefficient Differential Equations |
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| II. Second-order Linear Equations |
| 6 |
Second-order Linear Equations: Constant Coefficient, Homogeneous |
(PDF) |
(PDF) |
| 7 |
Second-order Linear Equations: Damping Conditions, Superposition, Initial Value Problems |
(PDF) |
(PDF) |
| 8 |
Superposition
Exponential Response |
(PDF) |
(PDF) |
| 9 |
Operators
Superposition
Undetermined Coefficients |
(PDF) |
(PDF) |
| 10 |
Resonance
Operators |
(PDF) |
(PDF) |
| 11 |
Review |
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| III. Short Topics |
| 12 |
Step and Delta |
(PDF) |
(PDF) |
| 13 |
Impulse Response = Weight Function and Convolution |
(PDF) |
(PDF) |
| IV. The Laplace Transform |
| 14 |
Laplace Transform
Poles |
(PDF) |
(PDF) |
| 15 |
Laplace Transform and ODEs |
(PDF) |
(PDF) |
| 16 |
Laplace Transform: Second-order Equations (Completing the Square)
t-shift Formula
Step and Delta Signals
Weight and Transfer
Convolution
Poles |
(PDF) |
(PDF) |
| 17 |
Laplace Transform: Meaning of the Pole Diagram
Euler's Method |
(PDF) |
(PDF) |
| V. Fourier Series |
| 18 |
Fourier Series |
(PDF) |
(PDF) |
| 19 |
Fourier Series: Differentiating, Integrating, Shifting, Stretching
Generalized Functions |
(PDF) |
(PDF) |
| 20 |
Review |
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| VI. First-order Systems |
| 21 |
Systems of First-order Equations2A |
(PDF) |
(PDF) |
| 22 |
Linear Systems |
(PDF) |
(PDF) |
| 23 |
Linear Phase Portraits |
(PDF) |
(PDF) |
| 24 |
Exponential Matrices |
(PDF) |
(PDF) |
| 25 |
Autonomous Systems |
(PDF) |
(PDF) |