18.03: Differential Equations. Spring, 2013
I. First-order differential equations
0
T 5 Feb
1
W 6 Feb
2
3
4
5
F 8 Feb
M 11 Feb
W 13 Feb
F 15 Feb
6
7
8
M 18 Feb
T 19 Feb
W 20 Feb
F 22 Feb
9
10
M 25 Feb
W 27 Feb
Recitation: Growth and decay models; separable equations:
EP 1.1, 1.4, Notes D.
Direction fields, existence and uniqueness of solutions:
EP 1.2, 1.3; Notes G.
Autonomous equations; the phase line, stability: EP 1.7, 7.1.
Numerical methods; fences and funnels: EP 6.1, 6.2.
Linear equations; variation of parameters: EP 1.5.
Linear equations as models. Solution by substitution: EP 1.5, 1.6.
PS1 due: covers Lectures 0–4
Presidents’ Day. Monday classes meet on Tuesday
Complex numbers, roots of unity: Notes C.1–3.
Complex exponentials; sinusoidal functions: Notes C.4, IR.6.
Input-response models; gain, phase lag: Notes IR (skip IR4 for now)
PS2 due: 5–7
Linearity and time invariance.
Hour Exam 1
II. Second-order linear equations
11
12
13
14
15
16
17
18
19
F 1 Mar
Characteristic polynomials; the spring-mass-dashpot model
EP 2.1 (skip Theorems 3, 4), 2.3 up to “Polyn. Operators”.
M 4 Mar
Complex roots; damping conditions: EP 2.3, 2.4.
W 6 Mar Driven systems: transients and superposition: EP 2.1 (Thms 2–4);
Notes O.1; EP 2.6 (157–159 only).
F 8 Mar
Operators; exponential response formula (ERF): Notes O.2, O.4.
PS3 due: 8–13
M 11 Mar Undetermined coefficients: EP 2.5 (144–153), Notes S
W 13 Mar Input-response models: EP 2.6, 2.7
F 15 Mar Applications in engineering
PS4 due: 13–16
M 18 Mar Stability and Resonance.
W 20 Mar Hour Exam 2
III. Fourier series, Laplace transform, Dirac delta function
20
F 22 Mar
Fourier series, coefficient formula, square wave: EP 8.1
25–29 Mar Spring Vacation
21 M 1 Apr
Convergence; sine and cosine series: EP 8.2, 8.3
22 W 3 Apr
Solving ODEs with Fourier series: EP 8.4
23 F 5 Apr
Rate of convergence, orthogonality, listening to Fourier series
PS 5 due: 17–22
24 M 8 Apr
Laplace transform: EP 4.1; Notes H
25 W 10 Apr Solving ODEs with the Laplace transform: EP 4.2, 4.3
26 F 12 Apr
Convolution: EP 4.4; Notes CG
PS 6 due: 23–25
15–16 Apr Patriots Day holiday
27 W 17 Apr Step functions and delta functions: EP 4.5; Notes IR.4
28 F 19 Apr
More about delta functions (including Fourier series): EP 4.6; Notes CG
29 F 22 Apr
Poles, stability, and resonance
PS 7 due: 26–28
30 W 24 Apr Hour Exam 3
IV. First order systems
31
32
33
34
F 26 Apr
M 29 Apr
W 1 May
F 3 May
35
36
37
M 6 May
W 8 May
F 10 May
38
39
M 13 May
W 15 May
Linear systems and matrices: EP 5.1–5.3, Notes LS.1.
Eigenvalues, eigenvectors: EP 5.4, Notes LS.2.
Complex eigenvalues, repeated eigenvalues: EP 5.4, 5.6; Notes LS.3.
Exponential matrix: EP 5.7; Notes LS.5, LS.6
PS8 due: 29–33
Inhomogeneous equations, variation of parameters: EP 5.8
Decoupling: Notes LS.4
Nonlinear systems: EP 7.2, 7.3; Notes GS
PS9 due: 34–36
Examples of nonlinear systems: EP 7.4, 7.5; Notes GS
Final Remarks.
Final Exam: Comprehensive 3-hour exam during final exam week; time and place TBA.
References:
EP: C. Henry Edwards and David E. Penney, Elementary Differential Equations with
Boundary Value Problems, Prentice-Hall, Sixth Edition. (Fifth edition will suffice.)
Notes: 18.03 Notes and Exercises available on line and from Graphic Arts (copies from
previous years will suffice).