| I. First-order Differential Equations |
| 1 |
Introduction
Separable Equations
Direction Fields |
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| 2 |
Isoclines
Models |
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| 3 |
Linear Equations |
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| 4 |
Autonomous Equations
The Phase Line |
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| 5 |
Complex Numbers
Complex Exponential |
Problem set 1 due |
| 6 |
Sinusoidal Functions |
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| 7 |
Sinusoidal System Response |
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| 8 |
Hour Exam I |
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| II. Second-order Linear Equations |
| 9 |
Solutions of Spring-mass-dashpot Models |
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| 10 |
Superposition
Initial Conditions |
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| 11 |
Damping Conditions
Inhomogeneous Equations |
Problem set 2 due |
| 12 |
Exponential Signals |
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| 13 |
Operator Notation and Undetermined Coefficients |
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| 14 |
Frequency Response |
Problem set 3 due |
| 15 |
Resonance |
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| 16 |
Review |
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| 17 |
Hour Exam II |
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| III. Delta Functions and Convolution |
| 18 |
Step and Delta Functions |
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| 19 |
Impulse Response and Convolution |
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| 20 |
From Convolution to the Laplace Transform |
Problem set 4 due |
| IV. The Laplace Transform |
| 21 |
Laplace Transform: Basic Properties |
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| 22 |
Application to ODEs
Partial Fractions |
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| 23 |
Completing the Square
Transforms of Delta and Time Translated Functions |
Problem set 5 due |
| 24 |
Convolution and Laplace Transform
The Pole Diagram |
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| 25 |
Numerical Methods |
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| V. Fourier Series |
| 26 |
Fourier Series |
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| 27 |
Differentiating and Integrating |
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| 28 |
General Period |
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| 29 |
Periodic Solutions |
Problem set 6 due |
| 30 |
Review: Fourier, Euler, Laplace |
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| 31 |
Hour Exam III |
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| VI. First-order Systems |
| 32 |
Linear Systems and Matrices |
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| 33 |
Eigenvalues
Eigenvectors |
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| 34 |
Complex or Repeated Eigenvalues |
Problem set 7 due |
| 35 |
Qualitative Behavior of Linear Systems |
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| 36 |
Normal Modes and the Matrix Exponential |
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| 37 |
Inhomogeneous Equations |
Problem set 8 due |
| 38 |
Nonlinear Systems
The Phase Plane |
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| 39 |
Examples of Nonlinear Systems |
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| 40 |
Final Exam |
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