Math198 Syllabus

Course description
This course will cover the rudiments of modern applied mathematics, including:
1. Contour Integration
  - Review Complex Variables
  - Definite integrals of elementary functions
  - Integral Representation of Functions
  - Special Functions
2. Asymptotic Expansions
  - Watson's Lemma
  - Stationary Phase and Steepest Descent Methods
  - Stoke's Phenomenon
  - Perturbation Analysis
  - Difference equations
  - ODE's
3. Elementary Partial Differential Equations of Mathematical Physics
  - Linear Evolution Equations
  - Fourier Transform Solutions
  - Phase Velocity and Group Velocity, Dispersion
  - Long-time Asymptotics of Fourier Integral Solutions of PDE's
Prerequisites:
Background in multivariable calculus, complex variables, elementary differential equations. With the widespread availability of powerful computer hardware and software, numerical methods have become an integral part of modern applied mathematics methods. While not a prerequisite, some familiarity with a programming language and a symbolic manipulator can be a useful complement to the course material.
Textbooks:
The material of the course will be based on class notes and several books. These will be placed on reserve at the Math/Phys Library. The main texts are:
- C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineer, McGraw-Hill.
- G.F. Carrier, M. Krook and C.E. Pearson, Functions of a Complex Variables, Hod Books.