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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.
Course readings.
| 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 |
|