67-376/576 APPLIED MATH ANALYSIS II:
FALL 2006
Section 01: 11:30-12:20 M W F Swart 3
INSTRUCTOR: Zoubir Benzaid
OFFICE: Swart 238 PHONE: 424-7354 (O) 236-9257 (H)
OFFICE HOURS: MTWF: 10:30-11:30 and MWF: 1:45-2:30 (And by appointment)
TEXTS:
Required: Partial Differential Equations and Boundary Value Problems with Applications by M. Pinsky, 3rd Edition, Waveland Press.
Recommended:
- Fourier Analysis with applications to Boundary Value Problems by M. Spiegel
- Fourier Series and Boundary Value Problems by Churchill & Brown.
- Applied Partial Differential Equations by R. Haberman
- Partial Differential Equations and Boundary Value Problems by N. Asmar.
- Advanced Engineering Mathematics by M. Greenberg.
- Mathematical Methods in the Physical Sciences by M. Boas.
TOPICS:
A detailed list of topics we will cover includes the following:
- Power Series Solutions and Special Functions: Method of Frobenius, Legendre functions and polynomials, Gamma function, Bessel functions, etc…
- Fourier Series, Fourier Transform and Sturm-Liouville Problem: Fourier coefficients, even and odd expansions, convergence of Fourier Series, Gibbs Phenomenon, Parseval’s Theorem and mean square error, orthogonality and general Fourier series, completeness.
- Boundary Value Problems in Rectangular, Cylindrical and Spherical Coordinates, Dirichlet, Neumann and Robbin Conditions.
- Diffusion or Heat Equation: Separation of Variables, Fourier and Laplace Transform methods
- Wave Equation: Vibrating String and Membrane, Separation of Variables, D’Alembert’s general solution.
- Laplace’s Equation: Harmonic functions, Poisson Formula.
- More Topics: Applications to Physics: Electrodynamics and Quantum Mechanics, Topics covered by students in their presentations.
SOFTWARE:
UWO has a full site license for the Computer Algebra System Maple. This software can be accessed using any PC or Mac at any computer lab on campus. Maple is extremely user friendly and I expect you will be using it to complete your homework and assigned projects. I will be giving demonstrations of the software and assigning various Maple projects throughout the semester.
WEBSITE: I will maintain a website for this course at http://www.uwosh.edu/faculty_staff/benzaid. The site will contain the syllabus, homework assignments, solutions to tests, solutions to selected homework problems, Maple worksheets, miscellaneous lecture notes and links to other interesting sites.
EXAMS:
There will be a mid-term exam (100 points), a final exam (100 points) and five sets of homework (20 points each) and class presentations (50 points). I will give the dates of the midterm and final exams in class.
GRADING: A: 90-100, AB: 86-89, B: 79-85, BC: 75-78, C: 65-74, CD: 60-64, D: 50-59, F: 0-49.
GRADUATE STUDENTS: The homework sets and tests will include a number of more challenging problems (computationally and/or theoretically)
MAKE-UPS:
Allowed only in emergency situations. Under no circumstances will a student be allowed to make up more than one exam.
GENERAL CLASS POLICY:
- Please relax, feel free to ask and answer questions and actively participate in the learning process.
- I do expect you to consult each other when working the homework problems; however what you submit must be your own work. To check that everyone is doing his/her share of work, I will be asking people to work some problems on office board.
- The homework sets constitute the most important part of the course. That is where, ideally, most of the learning is going to take place. You should write down your solutions very carefully. Be neat, write legibly and make full sentences. The end product should be work you are proud of. Do not use spiral paper. I will not accept papers that are illegible or just plain messy. Your papers will be graded on the basis of correctness of mathematics, logic, grammar and legibility.
- Attendance is almost MANDATORY. More than 4 absences will really hurt a student in a borderline situation.