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: Firstorder quasilinear equations.
Lagrange method and Characteristics. Classificationof linear second order PDEs.
Brief review of separation of variables. The onedimensional wave equation: its
solution and characteristics. Cauchy problem forthe wave equation. Laplace's
equation: The maximum principle, uniquenesstheorems. Green's function.
Neumann's function. The heat equation in onedimension.
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 (Finite Difference) 
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 
5.1 5.2 
The
Cauchy Problem and Initial Condition The
Weak Max. Principle 

11 
5.3 5.4 
Solutions on Bounded Intervals The
Heat Equation on real line 

12 
5.5 5.7 
The Heat equation on
the Halfline The Nonhomogeneous
Heat Equations 

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

13 
8.2 
Numerical Approximation of Solutions(Finite Element) Matlab and PDE toolbox 

14 
6.16 7.2 7.3 
Green's Function for a Dirichlet Problem A
Hilbert Space Approach Distributions and an
Existence Theorem +Lax Milgram Th. 

15 
6.17 
Conformal Mapping Technique Review and catchup 
