Lecture Notes
Below are the lecture notes for every lecture session. Some lecture sessions also have supplementary files called "Muddy Card Responses." Students pick up half pages of scrap paper when they come into the classroom, jot down on them what they found to be the most confusing point in the day's lecture or the question they would have liked to ask. Responses are then made available to all students on the class Web site.
| 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 | |
