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: 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 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
|
|||
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 (Finite Difference) |
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
|
|||
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 |
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 Half-line 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 catch-up |
|