| I. First-order Differential Equations |
| L0 |
Simple Models and Separable Equations |
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| R1 |
Natural Growth and Decay |
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| L1 |
Direction Fields, Existence and Uniqueness of Solutions |
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| R2 |
Direction Fields, Integral Curves, Isoclines |
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| L2 |
Numerical Methods |
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| L3 |
Linear Equations: Models |
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| R3 |
Numerical Methods; Linear Models |
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| L4 |
Solution of Linear Equations, Variation of Parameter |
Problem set 1 due |
| R4 |
First Order Linear ODEs: Models and Solutions |
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| L5 |
Complex Numbers, Complex Exponentials |
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| L6 |
Roots of Unity; Sinusoidal Functions |
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| L7 |
Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag |
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| R5 |
Complex Numbers, Complex Exponentials |
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| L8 |
Autonomous Equations; The Phase Line, Stability |
Problem set 2 due |
| L9 |
Linear vs. Nonlinear |
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| R6 |
Using the Complex Exponential; Autonomous Equations |
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| L10 |
Hour Exam I |
|
| II. Second-order Linear Equations |
| R7 |
Solutions to Second Order ODEs |
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| L11 |
The Spring-mass-dashpot model; Superposition
Characteristic polynomial; Real Roots; Initial Conditions |
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| L12 |
Complex Roots; Damping Conditions |
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| R8 |
Homogeneous Second Order Linear Equations |
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| L13 |
Inhomogeneous Equations, Superposition |
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| R9 |
Second Order Linear Equations |
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| L14 |
Operators and Exponential Signals |
Problem set 3 due |
| L15 |
Undetermined Coefficients |
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| R10 |
Operators, Exponential Response, Exponential Shift, Undetermined Coefficients |
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| L16 |
Frequency Response |
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| R11 |
Superposition, Frequency Response |
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| L17 |
Applications: Guest Appearance by EECS Professor Jeff Lang |
Problem set 4 due |
| L18 |
Exponential Shift Law; Resonance |
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| R12 |
Review |
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| L19 |
Hour Exam II |
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| III. Fourier Series |
| R13 |
Fourier Series: Introduction |
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| L20 |
Fourier Series |
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| L21 |
Operations on Fourier Series |
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| R14 |
Fourier Series: Playing Around |
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| L22 |
Periodic Solutions; Resonance |
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| R15 |
Fourier Series: Harmonic Response |
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| IV. The Laplace Transform |
| L23 |
Step Function and Delta Function |
Problem set 5 due |
| L24 |
Step Response, Impulse Response |
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| R16 |
Step and Delta Functions, and Step and Delta Responses |
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| L25 |
Convolution |
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| R17 |
Convolution |
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| L26 |
Laplace Transform: Basic Properties |
Problem set 6 due |
| L27 |
Application to ODEs; Partial Fractions |
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| R18 |
Laplace Transform |
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| L28 |
Completing the Square; Time Translated Functions |
Problem set 7 due |
| L29 |
Pole Diagram |
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| R19 |
Hour Exam Review |
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| L30 |
Hour Exam III |
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| V. First Order Systems |
| R20 |
Systems of First Order Equations |
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| L31 |
Linear Systems and Matrices |
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| L32 |
Eigenvalues, Eigenvectors |
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| R21 |
Eigenvalues and Eigenvectors |
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| L33 |
Complex or Repeated Eigenvalues |
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| R22 |
Complex or Repeated Eigenvalues |
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| L34 |
Qualitative Behavior of Linear Systems; Phase Plane |
Problem set 8 due |
| L35 |
Normal Modes and the Matrix Exponential |
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| R23 |
Qualitative Analysis of Linear Systems |
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| L36 |
Inhomogeneous Equations: Variation of Parameters Again |
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| R24 |
Matrix Exponentials and Inhomogeneous Equations |
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| L37 |
Nonlinear Systems |
Problem set 9 due |
| L38 |
Examples of Nonlinear Systems |
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| R25 |
Qualitative Analysis of Nonlinear Systems |
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| L39 |
Chaos |
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| R26 |
Review |
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| L40 |
Final Exam |
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