Contents
Catalog Links
Share

MA4322 Principles and Techniques of Applied Mathematics I

Selected topics from applied mathematics to include: Dimensional Analysis, Scaling, Stability and Bifurcation, Perturbation Methods- regular and singular with boundary layer analysis, as well as, asymptotic expansions of integrals, integrals equations, Green's functions of boundary value problems, and distribution theory.

Prerequisite

MA3042 and MA3132; MA3232 strongly recommended

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

By the end of this course, the student is expected to be able to:

  • Define and describe the properties of distributions and operations applied to them.
  • Be able to show distributional convergence of a sequence of distributions.
  • Be able to explain and apply the Poisson summation formula to transform an infinite series.
  • Know the difference between a generalized solution, classical solution, weak solution, and distributional solution of a linear differential equation L u = f
  • Know when a Green’s function exists, be able to construct elementary Green’s functions, and know how to use them to solve linear initial value and boundary value problems with arbitrary forcing.
  • Explain concepts of convergence within normed vector spaces, completeness of a vector space, and convergence of Cauchy sequences within vector spaces (Banach spaces).
  • Understand the Contraction Mapping Theorem and how it applies to integral and differential equations.
  • Explain the consequences of Brouwer’s fixed point theorem in finite dimensional space.
  • Explain the concepts of compactness and relative compactness, and how they are essential properties in the fixed point theorems of Schauder.
  • Understand concepts of orthogonal subspaces, best approximations and convergence of series representations of functions in infinite dimensional function space (Hilbert space), and functionals on normed and Hilbert spaces.
  • Be familiar with the idea of a space of bounded linear operators as a Banach space.
  • Understand adjoint operators and be able to construct them for boundary value problems as well as be able to determine the eigenvalues and eigenfunctions of such operators - both differential and integral.