| I. First-order Differential Equations |
| 1 |
Introduction
Separable Equations
Direction Fields |
EP 1.3
Notes G.1 (PDF)
SN §1 (PDF) |
| 2 |
Isoclines
Models |
EP 1.3, 1.4
SN §2 (PDF) |
| 3 |
Linear Equations |
EP 1.5
SN §3 (PDF) |
| 4 |
Autonomous Equations
The Phase Line |
EP 1.7, 7.1 |
| 5 |
Complex Numbers
Complex Exponential |
SN §5 (PDF)
SN §6 (PDF)
Notes C.1–3 (PDF) |
| 6 |
Sinusoidal Functions |
SN §4 (PDF)
Notes IR.6 (PDF) |
| 7 |
Sinusoidal System Response |
Notes IR.5 (PDF) |
| 8 |
Hour Exam I |
|
| II. Second-order Linear Equations |
| 9 |
Solutions of Spring-mass-dashpot Models |
EP 2.1, 2.3 |
| 10 |
Superposition
Initial Conditions |
EP 2.2
SN §9 (PDF) |
| 11 |
Damping Conditions
Inhomogeneous Equations |
For Damping Conditions
EP 2.4
For Inhomogeneous Equations
Notes O.1 (PDF)
EP 2.6 (pp. 158–159 only; see SN §7 (PDF) if you want to learn about beats) |
| 12 |
Exponential Signals |
SN §10 (PDF)
EP 2.6 (pp. 165–167) |
| 13 |
Operator Notation and Undetermined Coefficients |
SN §11 (PDF)
EP 2.5 (pp. 144–153)
Notes O.1, 2, and 4 (PDF) |
| 14 |
Frequency Response |
SN §13 (PDF)
SN §14 (PDF) |
| 15 |
Resonance |
SN §12 (PDF)
Notes O.3 (PDF) |
| 16 |
Review |
|
| 17 |
Hour Exam II |
|
| III. Delta Functions and Convolution |
| 18 |
Step and Delta Functions |
SN §16 (PDF) |
| 19 |
Impulse Response and Convolution |
SN §17 (PDF)
Notes I (PDF) |
| 20 |
From Convolution to the Laplace Transform |
|
| IV. The Laplace Transform |
| 21 |
Laplace Transform: Basic Properties |
EP 4.1 |
| 22 |
Application to ODEs
Partial Fractions |
SN §18 (PDF)
EP 4.2, 4.3 |
| 23 |
Completing the Square
Transforms of Delta and Time Translated Functions |
EP 4.5–4.6 |
| 24 |
Convolution and Laplace Transform
The Pole Diagram |
EP 4.4
SN §19 (PDF) |
| 25 |
Numerical Methods |
EP 6.1
Notes G (PDF) |
| V. Fourier Series |
| 26 |
Fourier Series |
EP 8.1 |
| 27 |
Differentiating and Integrating |
EP 8.3 |
| 28 |
General Period |
EP 8.2 |
| 29 |
Periodic Solutions |
EP 8.3, 8.4 |
| 30 |
Review: Fourier, Euler, Laplace |
|
| 31 |
Hour Exam III |
|
| VI. First-order Systems |
| 32 |
Linear Systems and Matrices |
EP 5.1–5.3
SN §23 (PDF)
Notes LS.1 (PDF) |
| 33 |
Eigenvalues
Eigenvectors |
EP 5.4
Notes LS.2 (PDF) |
| 34 |
Complex or Repeated Eigenvalues |
EP 5.4
Notes LS.3 (PDF) |
| 35 |
Qualitative Behavior of Linear Systems |
SN §24 (PDF) |
| 36 |
Normal Modes and the Matrix Exponential |
EP 5.7
Notes LS.6 (PDF) |
| 37 |
Inhomogeneous Equations |
EP 5.8 |
| 38 |
Nonlinear Systems
The Phase Plane |
EP 7.2, 7.3
Notes GS (PDF) |
| 39 |
Examples of Nonlinear Systems |
EP 7.4, 7.5
Notes GS (PDF) |
| 40 |
Final Exam |
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