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:

  • Final: The final is scheduled Tuesday, May 12th, 2-4pm in Bio West 210.
  • Midterm: The midterm is scheduled Thursday March 12th.
  • Homework: Homework will be collected every Thursday, and selected problems will be graded.
    Click here to see the Spring 99 homework assignments

  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