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