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Honors Differential Equations >> Content Detail



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Key to reading assignments:

(BR) are section numbers of Amazon logo Birkhoff, Garret, and Gian-Carlo Rota. Ordinary Differential Equations. 4th ed. New York, NY: Wiley, 1989. ISBN: 9780471860037.

(SN) are chapter numbers of 18.03 Supplementary Notes by Prof. Haynes Miller.

(Notes) refers to the PDFs in the lecture notes section.


LEC #TOPICSREADINGS
1Introduction, definitions and modeling

(BR) 1.1-1.2

(SN) 0-3

2First-order linear equations, separable equations(BR) 1.3-1.4
3First-order equations, Solution by quadrature

(BR) 1.5-1.7

(Notes) QD (PDF)

4The initial value problem, uniqueness; the algebra of complex numbers

(BR) 1.9-1.10

(SN) 5

5Second-order linear equations(BR) 2.1-2.2
6Undetermined coefficients

(SN) 11

7Stability criteria, the uniqueness theorem(BR) 2.3-2.4
8The Wronskian, sturm separation and comparison theorems(BR) 2.5-2.6
9Green's function I: Initial value problem(BR) 2.9
10Green's function II: Boundary value problem(BR) 2.10-2.11
11nth-order linear DEs with constant coefficients(BR) 3.1-3.3
12Basis of solutions, the uniqueness theorem(BR) 3.1-3.3
13Inhomogeneous equations, stability criteria(BR) 3.5-3.6
14Laplace transform: Basic properties(Notes) LT1 (PDF)
15Laplace transform techniques; step functions

(SN) 20

(Notes) LT1 (PDF)

16The Dirac delta and impulse functions, convolution

(SN) 17-19

(Notes) LT2 (PDF)

17Generalized functions, the pole diagram

(SN) 21-23

(Notes) LT2 (PDF)

18Plane autonomous systems

(BR) 5.1-5.4

(Notes) AS (PDF)

19Linear autonomous systems(BR) 5.4-5.5
20Wellposedness I(BR) 6.1-2 and 6.5
21Wellposedness II: Picard's iteration method(BR) 6.2 and 6.7-6.8
22Wellposedness III: Local theorems, Peano's existence theorem(BR) 5.3, 5.9, and 5.10
23Wellposedness IV: Strong continuity, bifurcation; exponential matrix

(BR) 5.4

(BR) Appendix A

(Notes) EX (PDF)

24Phase portraits I

(BR) 2.7, 3.3, and 5.5

(SN) 24-25

25Phase portraits II

(BR) 2.7, 3.3, and 5.5

(SN) 24-25

26Stability(BR) 5.7
27Methods of Lyapunov

(BR) 5.8

(Notes) LY (PDF)

28Damped and undamped pendulum

(BR) 5.9 and 5.11

(Notes) AS (PDF) and LY (PDF)

29Limit cycles

(BR) 5.12

(Notes) LC (PDF)

30Fourier series

(BR) 11.1

(Notes) FS (PDF)

31The heat equation(Notes) BV (PDF)
32The wave equation, the Laplace equation(Notes) BV (PDF)
33Sturm-Liouville systems(BR) 10.1-10.2 and 10.5-10.8
34-37ReviewsHandouts

 








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