Principles and Methods of Applied Mathematics

Math 583 A - Fall 1998

• Texts: A set of handwritten notes prepared two years ago by Dr. Tabor is available. The required textbook is
  • Principles of Applied Mathematics
    James P. Keener
    Addison-Wesley, 1988.

  Other recommended texts are
  • Linear Algebra
    Peter D. Lax
    Pure and Applied Mathematics, Wiley-Interscience Publication, John Wiley and Sons, New-York, 1997.

  • Complex Variables
    J. Ablowitz and Athanassios S. Fokas
    Cambridge Texts in Applied Mathematics, Cambridge University Press, 1997.

  • Principles and Techniques of Applied Mathematics
    Bernard Friedman
    Pure and Applied Mathematics, Dover Publication Inc., New-York, 1956

• Location:
  PAS 416 -- Now in MATH 501 --

  Time:

  Tuesdays and Thursdays, 2:00 - 3:15 pm

  Office Hours:

  Mondays 2-3 pm (in my office)

  Tuesdays 11-12 am (in the tutoring room -- Math Teaching Lab, Room 123)

  Tuesdays 5:30-6:30 pm (in my office; graduate students only)

  Wednesdays 11-12 am (in my office)

  or by appointment.

  Instructor: Dr. Joceline Lega

  Office: Mathematics 511

  Phone: 621-4350

  e-mail: lega@math.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 for Friday, December 18, 2-4pm in MATH 501.
    Solution
  • Midterm:
    The midterm is scheduled for Tuesday, October 13.
    Solution
  • Second midterm:
    The second midterm is scheduled for Tuesday, November 17.
    Solution
  • Homework:
    Homework will be collected every Thursday, and selected problems will be graded.
    Click here to see homework assignments

  Course description:

  • Review
    • Vector calculus
    • Linear algebra
      Proof of spectral theorem for square matrices
      Drill problems on linear algebra
    • Ordinary differential equations
      Drill problems on ordinary differential equations and answers

  • Complex variables and techniques of contour integration
    • Drill problems on complex numbers
    • Analytic functions
    • Multivalued functions and Riemann surfaces
    • Poles and residues
    • Cauchy's residue theorem and contour integration

  • A simple nonlinear partial differential equation
    • Intuition
    • Symmetries and scalings
    • Phase plane analysis and traveling wave fronts
    • Linearization about u=0

  • Fourier series
    • Definitions
    • Calculational aspects of Fourier series
    • Convergence issues

  • Distributions and the "delta function"
    • Delta sequences
    • Linear functionals and distributions
    • The "delta function" and its properties
    • Weak formulation of differential equations

  • Green's functions
    • Green's functions for first and second order ordinary differential equations
    • Solution of Poisson's equation

  Introduction to DSTOOL: Click here to download a short DSTOOL primer, in Postscript.