King Fahd University of Petroleum and
Minerals
Department
of Mathematics & Statistics
Syllabus Math 470
Semester
I, 20092010 (091)
Instructor:
Dr. Faisal AbdulKarim 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 p34 
2 
1.2 1.3 1.4 
Quasilinear first order equations, the Cauchy problem, Characteristic method, General solutions 
10, 11, 12p11 1, 3, 5 p1516 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, p116117 1, 3, 7,9 p8788
1, 5, 11, 14,15a p158 
"A+"
Monday


5 
4.3
6.1 6.2 6.4 
The Characteristic Triangle Domain of dependence and range of influence, WellPosedness. 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 p261262 
6 
6.5 3.6 6.9 8.2 
Existence Uniqueness and wellposed The Fourier Transform Dirichlet Problem Upper Halfplane (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 Halfplane (Fourier Integral) Dirichlet Problem Upper the Right QuarterPlane 
1, 6 p93 1, 4, p279 1 p282 
J
Eid
AlAdha Vacation: 19 Nov  4 Dec


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 halfplane 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 catchup 