| SES # | TOPICS | READINGS |
|---|---|---|
| I. First-order Differential Equations | ||
| L0 | Simple Models and Separable Equations | EP: 1.1 and 1.4 |
| L1 | Direction Fields, Existence and Uniqueness of Solutions | EP: 1.2 and 1.3 Notes: G.1 (PDF)# SN: 1 (PDF) |
| L2 | Numerical Methods | EP: 6.1 and 6.2 Notes: G.2 (PDF)# |
| L3 | Linear Equations: Models | EP: 1.5 SN: 2 (PDF) |
| L4 | Solution of Linear Equations, Variation of Parameter | EP: 1.5 SN: 3 (PDF) |
| L5 | Complex Numbers, Complex Exponentials | SN: 5 (PDF) SN: 6 (PDF) Notes: C.1-3 (PDF) |
| L6 | Roots of Unity; Sinusoidal Functions | SN: 4 (PDF) Notes: C.4 (PDF) and IR.6 (PDF)# |
| L7 | Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag | SN: 4 (PDF) Notes: IR.6 (PDF)# |
| L8 | Autonomous Equations; The Phase Line, Stability | EP: 1.7 and 7.1 |
| L9 | Linear vs. Nonlinear | |
| L10 | Hour Exam I | |
| II. Second-order Linear Equations | ||
| L11 | The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions | EP: 2.1, 2.2, and 2.3 upto "Polynomial Operators" SN: 9 (PDF) |
| L12 | Complex Roots; Damping Conditions | EP: 2.3 and 2.4 |
| L13 | Inhomogeneous Equations, Superposition | EP: 2.6, pp. 157-159 only, (See SN 7 (PDF) if you want to learn about beats) Notes: O.1 (PDF) |
| L14 | Operators and Exponential Signals | EP: 2.6, pp. 165-167 SN: 10 (PDF) Notes: O.1, 2, and 4 (PDF) |
| L15 | Undetermined Coefficients | EP: 2.5, pp. 144-153 SN: 11 (PDF) |
| L16 | Frequency Response | SN: 14 (PDF) |
| L17 | Applications: Guest Appearance by EECS Professor Jeff Lang | |
| L18 | Exponential Shift Law; Resonance | SN: 12 (PDF) Notes: O.3 (PDF) |
| L19 | Hour Exam II | |
| III. Fourier Series | ||
| L20 | Fourier Series | EP: 8.1 |
| L21 | Operations on Fourier Series | EP: 8.2 and 8.3 |
| L22 | Periodic Solutions; Resonance | EP: 8.3 and 8.4 |
| IV. The Laplace Transform | ||
| L23 | Step Function and Delta Function | SN: 17 (PDF) |
| L24 | Step Response, Impulse Response | SN: 18 (PDF) Notes: IR (PDF)# |
| L25 | Convolution | EP: 4.1 |
| L26 | Laplace Transform: Basic Properties | |
| L27 | Application to ODEs; Partial Fractions | EP: 4.2 and 4.3 SN: 20 (PDF) Notes: H |
| L28 | Completing the Square; Time Translated Functions | EP: 4.5-4.6 SN: 20 (PDF) |
| L29 | Pole Diagram | SN: 22 (PDF) |
| L30 | Hour Exam III | |
| V. First Order Systems | ||
| L31 | Linear Systems and Matrices | EP: 5.1-5.3 SN: 24 (PDF) Notes: LS.1 (PDF) |
| L32 | Eigenvalues, Eigenvectors | EP: 5.4 Notes: LS.2 (PDF) |
| L33 | Complex or Repeated Eigenvalues | EP: 5.4 Notes: LS.3 (PDF) |
| L34 | Qualitative Behavior of Linear Systems; Phase Plane | SN: 25 (PDF) |
| L35 | Normal Modes and the Matrix Exponential | EP: 5.7 Notes: LS.6 (PDF) |
| L36 | Inhomogeneous Equations: Variation of Parameters Again | EP: 5.8 |
| L37 | Nonlinear Systems | EP: 7.2 and 7.3 Notes: GS (PDF)# |
| L38 | Examples of Nonlinear Systems | EP: 7.4 and 7.5 Notes: GS (PDF)# |
| L39 | Chaos | |
| L40 | Final Exam | |
Table of Contents
Study Materials
Readings
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This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.
Listed in the table below are reading assignments for each lecture session.
"EP" refers to the course textbook: Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 5th ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 013145773X.
The 4th edition ( ISBN: 0130113018) differs slightly. If a reference to the Fourth Edition differs, I will indicate it by writing "IV: . . . ."
"SN" refers to the "18.03 Supplementary Notes" written by Prof. Miller.
"Notes" refers to the "18.03 Notes and Exercises" written by Prof. Mattuck.