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
AddisonWesley, 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 56 pm and Wednesdays 11am  1pm, or by appointment
 Instructor:
Dr. Joceline Lega
 Office: Economics 226
 Phone: 6264889
 email:
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 SturmLiouville theory
 Problems from quantum mechanics: discrete and continuous spectra
 Differential equations and integral equations
 Integral equations and the Fredholm alternative
 HilbertSchmidt 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 PoincaréLindstedt 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 EulerLagrange equations
 Functional differentiation
 Topics in Diffusive and Dispersive waves
 Quasilinear equations and method of characteristics
 Shocks
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