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# MATH 480 (Fall 2014): Partial Differential Equations

### Section and Class Number

Section 01 & 16295

Jing Li

### Contact information:

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)

### Final Exam

December 16, 2014, Tuesday 8:00 am - 10:00 am, Chaparral Hall Room 5119

### Midterm Exams

Midterm Exam 1: (date to be annouced) in class.
Midterm Exam 2: (date to be annouced) in class.

### Lecture times and locations

Tuesdays & Thursdays 9:30 am - 10:45 am in CR (Chaparral Hall) 5119

### Announcements

1. Course syllabus will be hand out in class on Aug 26, 2014.

### Course syllabus and tentative timetable

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;

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

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

17 Dec 16 Final Exam