Math 322 - Applied Mathematical Analysis

• Prerequisites: Math 319, 321.
• Frequency: Fall (I), Spring (II)
• Student Body: Students in the Sciences and Engineering. Applied Math majors.
• Credits: 3. (N-A)
• Recent Texts: Elementary Applied Partial Differential Equations, 3rd ed., by Richard Haberman.
• Course Coordinator: Fabian Waleffe
• Background and Goals: This is the second semester in the standard sequence in applied analysis at the math department. This sequence is aimed to applied math majors and students in the sciences and engineering who need to have knowledge of analysis and its applications beyond the standard calculus sequence. A good introductory course in the study of partial differential equations and boundary value problems.
• Alternatives: N/A
• Subsequent Courses: N/A

Content coverage:

• Introduction
  • General remarks on PDEs
  • Linearity and the Principle of Superposition
  • Separation of variables
  • An example of PDE: the heat equation
• Fourier Series
• Solution of the heat, Laplace and wave equations
• Finite Difference Methods: A First Look
• Inhomogeneous Equations
• A second look at the basic equations
  • Circular Domain
  • Higher dimensions
• Unbounded regions and the Fourier transform
• More on the wave equations: characteristics
• More on numerical methods
• Green's functions
• dispersion, stability, boundary layers