Principles and Methods
of Applied Mathematics
Math 583 B - Spring 1998
- Texts:
- A set of handwritten notes prepared last year by Dr. Tabor is
available. Recommended texts are listed below.
- Principles of Applied Mathematics
James P. Keener
Addison-Wesley, 1988.
- Advanced Mathematical Methods for Scientists and
Engineers
C. Bender and S. Orszag
McGraw Hill, 1978.
- Location:
- Bio West 210
- Time:
- Tuesdays and Thursdays, 2:00 - 3:15 pm
- Office Hours:
-
Tuesdays 5-6 pm and Wednesdays 11am - 1pm, or by appointment
- Instructor:
Dr. Joceline Lega
- Office: Economics 226
- Phone: 626-4889
- e-mail:
lega@acms.arizona.edu
- Grading Policy:
-
There will be one midterm and a final exam. Homework will count for 50%,
the midterm for 15% and the final exam for 35% of the semester grade.
- Exams:
- Course description: For an updated course
description, see the Spring 99 version
of this course
- Spectral Theory and Integral Equations
- Spectral theorem for symmetric matrices and the Fredholm
alternative
- Separation of variables and Sturm-Liouville theory
- Problems from quantum mechanics: discrete and continuous spectra
- Differential equations and integral equations
- Integral equations and the Fredholm alternative
- Hilbert-Schmidt kernels and their properties
- Eigenfunction expansions for differential operators
- Introduction to Perturbation Theory
- Perturbation expansions: O and o symbols
- Regular and singular perturbation theory for ordinary differential
equations
- Perturbation theory for eigenvalue problems
- Secularities and the Poincaré-Lindstedt method for
nonlinear oscillators
- Elementary Asymptotics
- Asymptotic expansion of integrals
- Watson's lemma
- Laplace's method
- Method of stationary phase
- Method of steepest descents
- Calculus of Variations and Functional Equations
- The Euler-Lagrange equations
- Functional differentiation
- Topics in Diffusive and Dispersive waves
- Quasi-linear equations and method of characteristics
- Shocks
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