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. 6th ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 9780136006138
[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.
Also listed are links to specially written Java™ applets, or Mathlets, that were used in the lecture session.
SES # | TOPICS | READINGS AND RELATED MATHLETS |
---|---|---|
I. First-order differential equations | ||
R1 | Natural growth, 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) Isoclines Mathlet |
L2 | Numerical methods |
[EP]: 6.1 and 6.2
[Notes]: G.2 (PDF) Euler’s method Mathlet |
L3 | Linear equations, models |
[EP]: 1.5
[SN]: 2 (PDF) |
L4 | Solution of linear equations, integrating factors |
[EP]: 1.5
[SN]: 3 (PDF) |
L5 | Complex numbers, roots of unity |
[SN]: 5 (PDF)
[SN]: 6 (PDF) [Notes]: C.1-3 (PDF) |
L6 | Complex exponentials; sinusoidal functions |
[SN]: 4 (PDF)
[Notes]: C.4 (PDF) and IR.6 (PDF) Complex roots Mathlet Complex exponential Mathlet |
L7 | Linear system response to exponential and sinusoidal input; gain, phase lag |
[SN]: 4 (PDF)
[Notes]: IR.6 (PDF) Trigonometric identity Mathlet |
L8 | Autonomous equations; the phase line, stability |
[EP]: 1.7 and 7.1
[SN]: Appendix A (PDF) Phase lines Mathlet |
L9 | Linear vs. nonlinear | [SN]: Appendix C (PDF) |
II. Second-order linear equations | ||
L11 | Modes and the characteristic polynomial |
[EP]: 2.1, 2.2, and 2.3 up to “Polynomial Operators”
[SN]: 9 (PDF) |
L12 | Good vibrations, damping conditions |
[EP]: 2.3 and 2.4
Damped vibrations Mathlet |
L13 | Exponential response formula, spring drive |
[EP]: 2.6, pp. 157-159
[SN]: 7 (PDF) (for beats) [Notes]: O.1 (PDF) Harmonic frequency response: Variable input frequency Mathlet |
L14 | Complex gain, dashpot drive |
[EP]: 2.6, pp. 165-167
[SN]: 10 (PDF) [Notes]: O.1, 2, 4 (PDF) |
L15 | Operators, undetermined coefficients, resonance |
[EP]: 2.5, pp. 144-153 and EP: 2.7 [SN]: 8 (PDF) [SN]: 11 (PDF) |
L16 | Frequency response |
[SN]: 14 (PDF)
Amplitude and phase: Second order II Mathlet Amplitude and phase: First order Mathlet |
L17 | LTI systems, superposition, RLC circuits. |
[SN]: Appendix B (PDF)
Series RLC circuit Mathlet |
L18 | Engineering applications |
[SN]: 12 (PDF)
[SN]: 13 (PDF) [Notes]: O.3 (PDF) |
III. Fourier series | ||
L20 | Fourier series |
[EP]: 8.1
[SN]: 16 (PDF) Fourier coefficients Mathlet |
L21 | Operations on fourier series | [EP]: 8.2 and 8.3 |
L22 | Periodic solutions; resonance | [EP]: 8.3 and 8.4 |
L23 | Step function and delta function | [SN]: 17 (PDF) |
L24 | Step response, impulse response |
[SN]: 18 (PDF)
[Notes]: IR (PDF) |
L25 | Convolution |
[SN]: 18 (PDF)
Convolution: Accumulation Mathlet Convolution: Flip and drag Mathlet |
L26 | Laplace transform: basic properties | [EP]: 4.1 |
L27 | Application to ODEs |
[EP]: 4.2 and 4.3
[SN]: 20 (PDF) [Notes]: H |
L28 | Second order equations; completing the squares |
[EP]: 4.5 and 4.6
[SN]: 20 (PDF) |
L29 | The pole diagram |
[EP]: 4.4
[SN]: 22 (PDF) [SN]: 23 (PDF) 18.03 Difference Equations and Z-Transforms (PDF)(Courtesy of Jeremy Orloff.) Amplitude response: Pole diagram Mathlet Poles and vibrations Mathlet |
L30 | The Transfer function and frequency response | |
IV. First order systems | ||
L32 | Linear systems and matrices |
[EP]: 5.1-5.3
[SN]: 25 (PDF) [Notes]: LS.1 (PDF) |
L33 | Eigenvalues, eigenvectors |
[EP]: 5.4
[Notes]: LS.2 (PDF) Linear phase portrait: Matrix entry Mathlet Matrix vector Mathlet |
L34 | Complex or repeated eigenvalues |
[EP]: 5.4
[Notes]: LS.3 (PDF) |
L35 | Qualitative behavior of linear systems; phase plane | [SN]: 26 (PDF) |
L36 | Normal modes and the matrix exponential |
[EP]: 5.7
[Notes]: LS.6 (PDF) |
L37 | Nonlinear systems |
[EP]: 7.2 and 7.3
[Notes]: LS.6 (PDF) |
L38 | Linearization near equilibria; the nonlinear pendulum |
[EP]: 7.4 and 7.5
[Notes]: GS (PDF) [SN]: Appendix B (PDF) [SN]: Appendix C (PDF) |
L39 | Limitations of the linear: limit cycles and chaos | Vector fields Mathlet |