Week
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Prerequisites
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Lecture Notes (Sections)
| Common Mistakes
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Q&A
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Homeworks
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1
(Jan. 9 -13)
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01 Separable Equations (2.1, 2.2)
02 Linear Equations (2.3)
03 Exact Equations (2.4)
| Separable, Linear, Exact
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QA01: Linear Equations
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HW1 (Sol) (Covers Chap. 2)
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2
(Jan. 16 - 20)
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04 Homogeneous and G(ax+by) (2.6)
05 Bernoulli and Linear Coefficients (2.6)
06 Constant-coefficient, Homogeneous, 2nd Order Equations (4.2)
| Homogeneous, Bernoulli, Constant Coefficient 2nd Order Linear
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QA02: Constant Coefficient 2nd Order Linear
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HW2 (Sol Updated Feb. 29)
(Covers 4.2 -- 4.5)
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3
(Jan. 23 - 27)
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07 Higher Order Equations (4.3)
08 Undetermined Coefficients (4.4)
09 Undetermined Coefficients (Cont.) (4.5)
| Constant Coefficient, Undetermined Coefficients
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No Question This Week
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HW3 (Sol Updated Feb. 23)
(Covers 4.6,4.7,8.5)
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4
(Jan. 30 - Feb. 3)
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Nothing new is needed.
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10 Variation of Parameters (4.6)
11 General 2nd Order Linear Equations (4.7)
12 Cauchy-Euler Equations (8.5)
| Variation of Parameters; Cauchy-Euler
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QA03: General 2nd Order Linear Equations
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HW4 (Sol)
(Covers 7.2 - 7.5)
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5
(Feb. 6 - 10)
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13 Laplace Transform (7.2)
14 Solving Equations (7.3)
15 More Equations (7.4)
| Laplace Transform Method
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QA04: Partial Fraction;
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HW5 (Sol)
Updated Feb. 10, Added one Prob on Periodic Functions.
(Covers 7.6 - 7.9)
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6
(Feb. 13 - 17)
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Nothing New is Needed.
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16 More Equations (7.5, 7.9)
17 Discontinuous and Periodic Functions (7.6)
18 Convolution (7.7)
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7
(Feb. 27 - Mar. 2)
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Nothing New is Needed.
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19 Impulse Function (7.8)
Midterm Review (All Sections)
Mid Rev Sol 1
Mid Rev Sol 2
20 Review: Chapter 4 & 8.5
21 Review: Chapter 2
(Updated 3pm, Mar 2)
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8
(Mar. 5 - 9)
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22 Power Series Method (8.2)
23 Radius of Convergence; Examples (8.3)
24 More Examples (8.4)
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HW6 (Sol)
Updated Mar. 7, added 3 new problems
Updated Mar. 22, a typo in (59) fixed
(Covers 8.2 - 8.4)
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9
(Mar. 12 - 16)
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25 Partial Differential Equations: Introduction and Overview of Chapter 10(10.1)
26 Boundary Value Problems (10.2)
27 Separation of Variables: Simple Cases (10.2)
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HW7 (Sol)
(Covers 10.1 - 10.4)
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10
(Mar. 19 - 23)
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28 Sturm-Liouville Theory (10.3)
29 Fourier Series (10.3)
30 Fourier Sine and Cosine Series (10.4)
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HW8 (Sol)
Updated Apr. 4, Sol to 1st problem corrected
(Covers 10.3 - 10.5)
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11
(Mar. 26 - 30)
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31 Heat Equation with Dirichlet Boundary Conditions (10.5)
32 Heat Equation with Neumann Boundary Conditions (10.5)
33 Heat Equation with Non-homogeneous Boundary Conditions (10.5)
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12
(Apr. 2 - 4)
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34 Nonhomogeneous Heat Equations (10.5)
35 Heat Equations with Other Boundary Conditions (10.5)
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HW9 (Sol)
Updated Apr. 19. Typos in Prob3 Corrected
(Covers 10.5)
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13
(Apr. 11 - 13)
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36 Review of Chapter 8 (Power Series)
37 Review of 7.7-7.9 (Laplace Transform)
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