| SES # | TOPICS | |
|---|---|---|
| I. First-order Differential Equations | ||
| L0 | Simple Models and Separable Equations | |
| L1 | Direction Fields, Existence and Uniqueness of Solutions (PDF) | |
| L2 | Numerical Methods (PDF) | |
| L3 | Linear Equations: Models (PDF) | |
| L4 | Solution of Linear Equations, Variation of Parameter (PDF) | |
| L5 | Complex Numbers, Complex Exponentials (PDF) | |
| L6 | Roots of Unity; Sinusoidal Functions (PDF) | |
| L7 | Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag (PDF) | |
| L8 | Autonomous Equations; The Phase Line, Stability (PDF) Muddy Card Responses (PDF) | |
| L9 | Linear vs. Nonlinear (PDF) | |
| L10 | Hour Exam I | |
| II. Second-order Linear Equations | ||
| L11 | The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions (PDF) Muddy Card Responses (PDF) | |
| L12 | Complex Roots; Damping Conditions (PDF) | |
| L13 | Inhomogeneous Equations, Superposition (PDF) | |
| L14 | Operators and Exponential Signals (PDF) Muddy Card Responses (PDF) | |
| L15 | Undetermined Coefficients (PDF) | |
| L16 | Frequency Response (PDF) | |
| L17 | Applications: Guest appearance by EECS Professor Jeff Lang (PDF) Supplementary Notes Driving Through the Dashpot (PDF) | |
| L18 | Exponential Shift Law; Resonance (PDF) | |
| L19 | Hour Exam II | |
| III. Fourier Series | ||
| L20 | Fourier Series (PDF) | |
| L21 | Operations on Fourier series (PDF) Muddy Card Responses (PDF) | |
| L22 | Periodic Solutions; Resonance (PDF) | |
| IV. The Laplace Transform | ||
| L23 | Step Function and delta Function (PDF) | |
| L24 | Step Response, Impulse Response (PDF) | |
| L25 | Convolution (PDF) | |
| L26 | Laplace Transform: Basic Properties (PDF) Muddy Card Responses (PDF) | |
| L27 | Application to ODEs; Partial Fractions (PDF) | |
| L28 | Completing the Square; Time Translated Functions (PDF) Muddy Card Responses (PDF) | |
| L29 | Pole Diagram (PDF) | |
| L30 | Hour Exam III | |
| V. First Order Systems | ||
| L31 | Linear Systems and Matrices (PDF) | |
| L32 | Eigenvalues, Eigenvectors (PDF) | |
| L33 | Complex or Repeated Eigenvalues (PDF) | |
| L34 | Qualitative Behavior of Linear Systems; Phase Plane (PDF) | |
| L35 | Normal Modes and the Matrix Exponential (PDF) | |
| L36 | Inhomogeneous Equations: Variation of Parameters Again (PDF) Muddy Card Responses (PDF) | |
| L37 | Nonlinear Systems (PDF) | |
| L38 | Examples of Nonlinear Systems (PDF) | |
| L39 | Chaos (PDF) | |
| L40 | Final Exam | |