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Section 01 & 16295
Jing Li
Office: Live Oak Hall (LO), Room 1303C
Phone: 818-677-7799
E-mail: jing.li(at)csun(dot)edu
Office hours: Tuesdays & Thursdays 11:00 am - 12:00 pm or by
appointment (email)
December 16, 2014, Tuesday 8:00 am - 10:00 am, Chaparral Hall Room 5119
Midterm Exam 1: (date to be annouced) in class.
Midterm Exam 2: (date to be annouced) in class.
Tuesdays & Thursdays 9:30 am - 10:45 am in CR (Chaparral Hall) 5119
Introduction to Partial differential Equations by Peter J. Olver.
I will post all assigments, solutions and additional material in this
space. You should therefore consult this spot frequently.
Course Syllabus
| Week | Date | Topics covered | Homework | Homework due date | Practice Problems | Additional Material |
|---|---|---|---|---|---|---|
| 1 | Aug 26 & 28 | Chapter 1: What Are Partial Differential Equations? Sec. 2.1: Stationary Waves |
Exercises Chapter 1 (page
4): 1.1, 1.2, 1.4; (page
8): 1.5, 1.10,
1.12, 1.16; (page
13): 1.17, 1.18, 1.19, 1.20, 1.22, 1.25,
1.26, 1.27(a), (b), 1.28(b), (d);
Exercises 2.1 (page 18): 2.1.1, 2.1.3 (a), (c), (e), 2.1.4, 2.1.5, 2.1.9; |
(Exercises Chapter 1: due Sept 4, extended to be due Sept 9)
(Exercises 2.1 due Sept 11) |
Exercises Chapter 1 (page
4): 1.3; (page 8):1.6, 1.8 (a), 1.11, 1.13; (page 13):
1.21, 1.23, 1.24, 1.27(c), 1.28(a), (c), (e);
Exercises 2.1 (page 18):2.1.2, 2.1.3 (b), (d), 2.1.6, 2.1.7, 2.1.8; |
|
| 2 | Sept 2 & 4 |
Sec. 2.2: Transport and Traveling Waves
Uniform Transport Transport with Decay Nonuniform Transport |
Exercises 2.2 (page 23): 2.2.1, 2.2.2 (a), (c), 2.2.3 (b), (d), 2.2.4, 2.2.6, 2.2.9; (page 30): 2.2.16, 2.2.17, 2.2.20, 2.2.22, 2.2.23, 2.2.25, 2.2.26, 2.2.27; | (Exercises 2.2 due Sept 18) | Exercises 2.2 (page 23):2.2.2 (b), (d), 2.2.3 (a), (c), 2.2.5, 2.2.7, 2.2.10, 2.2.11, 2.2.14; (page 30): 2.2.24, 2.2.28, 2.2.29, 2.2.30; |
|
| 3 | Sept 9 & 11 |
Sec. 2.3: Nonlinear Transport and Shocks
Sec. 2.4: The Wave Equation: d'Alembert s Formula |
Exercises 2.3 (page 47):
2.3.3, 2.3.6
(a);
Exercises 2.4 (page 60): 2.4.1, 2.4.4 (b), (d), 2.4.7, 2.4.8, 2.4.9, 2.4.13, 2.4.17; |
(Exercises 2.3 due Sept 24)
(Exercise 2.4 due Sept 30) |
Exercises 2.3 (page
47): 2.3.4, 2.3.5, 2.3.14; Exercises 2.4 (page 60): 2.4.2, 2.4.3, 2.4.4 (a), (c), (e), 2.4.6, 2.4.9 (b), 2.4.10, 2.4.11, 2.4.14, 2.4.20, 2.4.21; |
|
| 4 | Sept 16 & 18 |
Sec. 3.1: Eigensolutions of Linear Evolution Equations
The Heated Ring Sec. 3.2: Fourier Series Periodic Extensions Piecewise Continuous Functions |
Exercises 3.1 (page 72):
3.1.1 (b), (e),
3.1.2 (a), 3.1.4 (b), 3.1.5;
Exercises 3.2 (page 76): 3.2.1 (a),(b),(d),(f), 3.2.2 (b),(d), 3.2.5; (Page 78): 3.2.6 (b),(d),(h), 3.2.9; (Page 81): 3.2.14 (a),(d),(f),(i), 3.2.15 (a),(e), 3.2.18, 3.2.21, 3.2.23; |
(Exercises 3.1 due Oct 2)
(Exercises 3.2 due Oct 14) |
Exercises 3.1 (page
72): 3.1.1 (a), (c), (d), 3.1.2 (b), (c), 3.1.3, 3.1.4 (a), (c),
3.1.6;
Exercises 3.2 (page 76):3.2.1 (c),(e),(g),(h), 3.2.2 (a), (c), (e), 3.2.3, 3.2.4; (Page 78):3.2.6 (a),(c),(e),(f),(g),(i), 3.2.7, 3.2.10-3.2.12; (Page 81):3.2.14 (b),(c),(e),(g),(h),(j),(k), 3.2.15 (b),(c),(d),(f), 3.2.16, 3.2.19, 3.2.20, 3.2.22, 3.2.24; |
|
| 5 | Sept 23 & 25 |
Sec. 3.2 cont'd
The Convergence Theorem Even and Odd Functions Complex Fourier Series Quiz 1 |
Exercises 3.2 (Page 84): 3.2.5; (Page 87): 3.2.31 (a),(c),(e), 3.2.39, 3.2.40 (a), 3.2.41 (a),(c), 3.2.42, 3.2.48; (Page 91): 3.2.51 (a),(c),(e), 3.2.52, 3.2.53, 3.2.60; | (Exercises 3.2 due Oct 14) | Exercises 3.2 (Page 84):3.2.26, 3.2.27, 3.2.29, 3.2.30; (Page 87):3.2.32-38, 3.2.40 (b), 3.2.41 (b),(d), 3.2.43-46, 3.2.50; (Page 91):3.2.51 (b),(d),(f),(g), 3.2.54-59, 3.2.61; | |
| 6 | Sept 30 & Oct. 2 |
Sec. 3.3: Differentiation and Integration
Integration of Fourier Solutions Differentiation of Fourier Solutions Sec. 3.4: Change of Scale |
Exercises 3.3 (page 95):
3.3.1 (a),
3.3.2, 3.3.4 (a);
Exercises 3.4 (page 97): 3.4.1 (a), 3.4.2 (c), 3.4.3 (b), (d); |
(Exercises 3.3 due Oct 21)
(Exercises 3.4 due Oct 21) |
Exercises 3.3 (page
95):3.3.1 (b), 3.3.3, 3.3.4 (b), 3.3.5, 3.3.6, 3.3.8;
Exercises 3.4 (page 97): 3.4.1 (b), 3.4.2 (a), (b), (d), 3.4.3 (a), (c), (e), 3.4.4--3.4.6, .3.3.8--3.3.10; |
|
| 7 | Oct 7 & Oct 9 |
Sec. 4.1 The Diffusion and Heat Equations
The Heat Equation Smoothing and Long Time Behavior The Heated Ring Redux |
Exercises 4.1 (page 138): 4.1.1, 4.1.4, 4.1.7, 4.1.10 (a),(c), 4.1.13, 4.1.16 (a),(b); | (Exercises 4.1 due Oct. 28) | Exercises 4.1 (page 138):4.1.2, 4.1.3, 4.1.5, 4.1.6, 4.1.8, 4.1.9, 4.1.10 (b), (d), 4.1.11, 4.1.14, 4.1.15, 4.1.17-20. | |
| 8 | Oct 14 & 16 |
Sec. 4.1 cont'd:
Inhomogeneous Boundary Conditions Sec. 4.2 The Wave Equation Separation of Variables and Fourier Series Solutions Quiz 2 |
Exercises 4.2 (page 145): 4.2.3 (b),(d),(f), 4.2.4 (b), 4.2.6, 4.2.10, 4.2.11; | (Exercises 4.2 (page 145) due Oct. 30) | Exercises 4.2 (page 145): 4.2.2, 4.2.3 (a), (c), (e), (g), 4.2.4 (a), 4.2.5, 4.2.7, 4.2.8, 4.2.9, 4.2.12. | |
| 9 | Oct 21 & 23 |
Sec. 4.2 cont'd:
The d'Alembert Formula for Bounded Intervals Sec. 4.3: The Planar Laplace and Poisson Equations Separation of Variables |
Exercises 4.2 (page 149):
4.2.13, 4.2.16, 4.2.22, 4.2.25, 4.2.28, 4.2.29 (a), (b), 4.2.31, 4.2.32, 4.2.34 (a), 4.2.35.
Exercises 4.3 (page 154): 4.3.2, 4.3.4, 4.3.6 |
(Exercises 4.2 (page 149) due Nov. 13)
(Exercises 4.3 (page 154) due Nov. 18) |
Exercises 4.2 (page 149):
4.2.14 (a), (c), 4.2.15 (a), (c), 4.2.17, 4.2.18, 4.2.23, 4.2.24, 4.2.26, 4.2.27, 4.2.30, 4.2.33, 4.2.34 (b), 4.2.36, 4.2.37.
Exercises 4.3 (page 154): 4.3.7, 4.3.8. |
|
| 10 | Oct 28 & 30 |
Sec. 4.3 cont'd:
Polar Coordinates Midterm 1 |
Exercises 4.3 (page 159): 4.3.10 (b), (d), 4.3.12 (a), 4.3.13 (b), 4.3.15 | (Exercises 4.3 (page 159) due Nov. 18) | Exercises 4.3 (page 159): 4.3.10 (a),(c), 4.3.11, 4.3.12 (b), (d), 4.3.13(a),(d), 4.3.14, 4.3.16, 4.3.17, 4.3.18, 4.3.19, 4.3.20. | |
| 11 | Nov 4 & 6 |
Sec. 4.3 Cont'd:
Averaging, the Maximum Principle, and Analyticity Sec. 4.4: Classification of Linear Partial Differential Equation |
Exercises 4.3 (page 169):
4.3.22 (a),
(c), 4.3.25 (a), 4.3.27 (a),(b), 4.3.33, 4.3.34(b),(d),
4.3.40, 4.3.46
Exercises 4.4 (page 173): 4.4.1 (b),(d), 4.4.2 (a),(c),(e), 4.4.3, 4.4.6, 4.4.11. |
(Exercises 4.3 (page 169) due Nov. 18)
(Exercises 4.4 due Nov. 20) |
Exercises 4.3 (page
169): 4.3.22 (b),(d),(f), 4.3.23, 4.3.24, 4.3.25 (b),(c), 4.3.26,
4.3.27 (c), 4.3.28, 4.3.29, 4.3.30-4.3.32, 4.3.34 (a),(c),(e),(f),(g),
4.3.39, 4.3.42-4.3.34, 4.3.48
Exercises 4.4 (page 173): 4.4.1 (a),(c),(e), 4.4.2 (b),(d),(f), 4.4.4, 4.4.5, 4.4.7, 4.4.8, 4.4.9, 4.4.20, 4.4.12, 4.4.13. |
|
| 12 | Nov 11 & 13 |
Veterans' Day Holiday, no Class on Tuesday
Sec. 6.1: Generalized Functions |
Exercises 6.1 (page 227):
6.1.1
(a),(c),(e), 6.1.2 (a),(c), 6.1.4 (a), 6.1.5 (b), 6.1.6 (b),(f),
6.1.9, 6.1.13, 6.1.19; (page 233):
6.1.27, 6.1.36
;
|
(Exercises 6.1 due Dec. 2)
|
Exercises 6.1 (page
227): 6.1.1 (b),(d),(f), 6.1.2 (b), (d)-(f), 6.1.3, 6.1.4 (b)-(d),
6.1.5 (a),(c), 6.1.6 (a),(c),(d),(e),(g), 6.1.7, 6.1.8, 6.1.10,
6.1.11, 6.1.12, 6.1.17, 6.1.18, 6.1.21, 6.1.22; (page 233):
6.1.28, 6.1.34, 6.1.37;
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|
| 13 | Nov 18 & 20 |
Sec. 6.2: Green's Functions for One-Dimensional Boundary
Value Problems
Sec. 6.3: Green's Functions for the Planar Poisson Equation Calculus in the Plane The Two-Dimensional Delta Function The Green's Function |
Exercises 6.2 (page 240):
6.2.1, 6.2.3,
6.2.4, 6.2.13;
Exercises 6.3 (page 255): 6.3.1, 6.3.5, 6.3.9, 6.3.10; |
(Exercises 6.2 due Dec. 9)
(Exercises 6.3 due Dec. 9) |
Exercises 6.2 (page
240):6.2.2, 6.2.5, 6.2.7, 6.2.9, 6.2.10, 6.2.11;
Exercises 6.3 (page 255): 6.3.3, 6.3.4, 6.3.6, 6.3.11, 6.3.12; |
|
| 14 | Nov 25 & 27 |
Sec. 6.3: cont'd
The Method of Images
Thanksgiving Recess, no Class on Thursday |
Exercises 6.3 (page 259):
6.3.20, 6.3.23,
6.3.25, 6.3.27, 6.3.31 (a), (b)
|
Exercises 6.3
(page 259): 6.3.15, 6.3.17, 6.3.18, 6.3.21, 6.3.29
|
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|
| 15 | Dec 2 & 4 |
Sec. 7.1: The Fourier Transform
Sec. 7.2: Derivatives and Integrals Midterm 2 |
Exercises 7.1 (page 273):
7.1.1
(b),(d),(f), 7.1.2 (b),(d), 7.1.3 (a),(b), 7.1.5, 7.1.10,
7.1.13, 7.1.16 (a),(b)
Exercises 7.2 (page 277): 7.2.1 (a),(b),(d),(e), 7.2.2 (a), 7.2.3 (b),(d), 7.2.5 (a),(b), 7.2.8, 7.2.9 (a),(c), 7.2.11 |
|
Exercises 7.1 (page
273): 7.1.1 (a),(c),(e),(g), 7.1.2 (a),(c),(e), 7.1.3 (c),
7.1.7, 7.1.9, 7.1.12, 7.1.14, 7.1.16 (c), 7.1.17-7.1.20.
Exercises 7.2 (page 277): 7.2.1 (c),(f), 7.2.2 (b), 7.2.3 (a),(c),(e), 7.2.5 (c),(d), 7.2.9 (b),(d), 7.2.12-7.2.14 |
Solutions for Midterm 2 |
| 16 | Dec 9 | Sec. 7.3: Green's Functions and Convolution |
Exercises 7.3 (page 280): 7.3.1 (a),(c), 7.3.3 (b), 7.3.4, 7.3.6; (page 283): 7.3.10 (a),(b), 7.3.12, 7.3.14, 7.3.15 (a),(c), 7.3.22 (b),(d) |
Exercises 7.3 (page 280): 7.3.1 (b),(d), 7.3.3 (a),(c), 7.3.5, 7.3.8; (page 283): 7.3.11, 7.3.15 (b),(d), 7.3.18, 7.3.20, 7.3.22 (a),(c),(e), 7.3.24 |
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| 17 | Dec 16 | Final Exam |