Math 704: Spring 2001
Methods of Applied Mathematics-2
Fabian Waleffe
Day |
Time |
Place |
TR |
9:30-10:45pm |
B305 Van Vleck Hall |
Take Home exam #1 Due 9:30 am Thur Feb 22, 2001
Take Home exam #2 Due 9:30 am Thur Apr 12, 2001
Exam #2 SOLUTIONS Thur Apr 26, 2001
Take Home exam #3 Due 11:11 am Fri May 11, 2001
Handouts
Fourier transform, series and discrete Fourier transform
REFERENCES:
- Partial Differential Equations of Applied Mathematics,
Erich Zauderer, 2nd Ed., Wiley-Interscience 1989. [Graduate, Textbook]
- Elementary Applied Partial Differential Equations,
Richard Haberman, THIRD Edition, Prentice-Hall 1998. [Undergrad-Grad Textbook,
Separation, Green's functions background, Chap 12-14: graduate applied Math]
- Linear and Nonlinear waves , G.B. Whitham, Wiley 1974.
[Research Monograph, a classic]
- Partial Differential Equations , R. McOwen, Prentice-Hall 1996.
[Not applied math, but nice concise overview]
- Similarity, Self-Similarity and Intermediate Asymptotics,
G.I. Barenblatt, Cambridge [Research Monograph]
Description
This is basically a course on partial differential equations taught from
an applied mathematics view point. We'll look briefly at where the equations
come from and discuss their validity and limitations. We'll look at the
properties and methods of solutions of various types of equations, both
linear and nonlinear. The methods will be mostly analytical but we'll
also look at asymptotic techniques. There will be little discussion
of numerical methods (for that see e.g. CS/Math 712, 713).
Students should have had a course on differential equations ( e.g.
Math 319) and, ideally, one on partial differential equations
( e.g. Math 322). A basic knowledge of general physics (especially
mechanics, thermodynamics and electromagnetism) is expected.
We'll cover Chapters 2 and 3 in Zauderer pretty completely
and sample the rest of the book.
- Introduction: conservation laws, constitutive laws, basic PDEs
- First order PDEs, characteristics, traffic flow, eikonal equation,
Hamilton-Jacobi.
- Random walks and diffusion
- Classification of PDEs, well-posedness;
gas dynamics, shallow-water equations
- Separation of variables, Sturm-Liouville, Fourier series and
transforms. Duhamel's principle. Similarity solutions.
- Green's functions, distributions
- Equations of Fluid Mechanics, Electromagnetism and Elasticity:
Navier-Stokes, Maxwell, Navier.
- Perturbation and asymptotic methods; boundary layers, geometrical
optics
Grading
Two in-class exams, at least two take-homes. NO FINAL.
Office hours: by appointment.