18.03 | Spring 2010 | Undergraduate

Differential Equations


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.

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)

Amplitude and phase: Second order II Mathlet

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

Amplitude and phase: Second order III 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

Fourier coefficients: Complex with sound Mathlet

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)

Linear phase portrait: Matrix entry Mathlet

L35 Qualitative behavior of linear systems; phase plane [SN]: 26 (PDF)

Linear phase portrait: Matrix entry Mathlet

Linear phase portrait: Cursor entry Mathlet

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

Course Info

As Taught In
Spring 2010
Learning Resource Types
Lecture Videos
Lecture Notes
Problem Sets with Solutions