King Fahd University of Petroleum and Minerals

Department of Mathematics & Statistics

Syllabus Math 470

Semester I, 2009-2010 (091)

Instructor: Dr. Faisal Abdul-Karim Fairag

Course:             Math 470 (Partial Differential Equations)

Text Book:         Beginning Partial Differential Equation. by P. O’Neil.

Reference: Applied partial Differential Equations by John Ockendon

Objectives:         First order quasilinear equations. Lagrange method and Characteristics. Classification of linear second order PDEs. Brief review of separation of variables. The one dimensional wave equation: its solution and characteristics. Cauchy problem for the wave equation. Laplace's equation: The maximum principle, uniqueness theorems. Green's function. Neumann's function. The heat equation in one dimension.

Week

Sec

## Topic

Suggested

Homework

1

1.1

Introduction, Linear first order PDE’s, Characteristics

2, 4, 7, 8 p3-4

2

1.2

1.3

1.4

Quasilinear first order equations, the Cauchy problem, Characteristic method, General solutions

10, 11, 12p11

1, 3, 5 p15-16

1, 3, 5, 7, 9, p22

3

2.1

2.2

2.3

2.4

Second order PDE’s in two variables: Classification by characteristics, Canonical forms, Second order Cauchy problem

1, 3, 5, 7, 9, page25

2(a, c), 3, p29

2, 3, p33

1, 3, 5, 6, p36

7, 9, p37

4

2.5

4.1

3.4

4.8

The wave equation in 1D: The Cauchy problem and d’Alembert’s formula,

Review of  Fourier series and sine and cosine expansion

The wave equation: Fourier Series Solutions, Separation of variables.

1 p45

3, 5, 9, 10, 13, p116-117

1, 3, 7,9  p87-88

1, 5, 11, 14,15a  p158

# "A+"Monday 26 Oct, 2009: Exam I,  6:00 PM "A+"

5

4.3

6.1

6.2

6.4

The Characteristic  Triangle  Domain of dependence and range of influence, Well-Posedness.

Dirichlet and Neumann ( setting the Problem)

Some Harmonic Functions

Maximum Principle & Mean value property

1, 2 p130

170 p266

8 p246

3, 4, 5, 6, p250

4, 6 p261-262

6

6.5

3.6

6.9

8.2

Existence Uniqueness and well-posed

The Fourier Transform

Dirichlet Problem Upper Half-plane (Fourier Transform)

Numerical Approximation of  Solutions

1  p266

3, 12, 15, 22 p101

7

3.5

6.9

6.10

The Fourier Integral

Dirichlet Problem Upper Half-plane (Fourier Integral)

Dirichlet Problem Upper the Right Quarter-Plane

1, 6 p93

1, 4, p279

1 p282

# J Eid Al-Adha Vacation: 19 Nov - 4 Dec, 2009 J

8

6.7

6.12

6.13

Dirichlet Problem for a disk

The Neumann Problem

The Neumann Problem for a Rectangle

4, 6 p271

9

6.15

6.14

The Neumann Problem for the upper half-plane

The Neumann Problem for a disk

"A+"   Saturday, 12 Dec 2009: Exam II,   6:00PM  "A+"

10

6.16

7.2

7.3

Green's Function for a Dirichlet Problem

A Hilbert Space Approach

Distributions and an Existence Theorem

11

12

"A+"   Monday 4 Jan, 2009 : Exam III,   6:00PM   "A+"

13

14

15

Review and catch-up

• The date of the final exam will be announced by the Registrar. The Final Exam is comprehensive.