Math 5434

Principles and Techniques of Applied Mathematics

Offered in the Fall semester of odd years.

Course Description

From Catalog:

Mathematical principles and numerical techniques for analytically and numerically solving ordinary and partial differential equations. This includes mathematical principles behind finite element software such as quadrature rules, numerical linear algebra, stiff ODE solvers, and solving nonlinear systems of equations. High-level programming language required. I

This one semester course will cover a number of mathematical principles that lead to clearer analytic reasoning and better understanding of computational algorithms and software. A list of topics include:

  • Inner product spaces (20%)
    • Orthogonal Polynomials
    • Weighted Least-Squares
    • Development of Quadrature Formula
    • Basics of Finite Element Methods
  • Numerical Linear Algebra (20%)
    • Matrix Factorizations
    • Working with Sparse Matrices
    • Iterative Methods
    • Eigenvalue Problems and the SVD
  • Ordinary Differential Equations (15%)
    • Variation of Parameters Formula
    • Linear Stability Analysis
    • Numerical Methods for ODEs
  • Nonlinear Equations and Optimization (30%)
    • Fixed Point Iterations
    • Newton's Method and Extensions
    • Numerical and Automatic Differentiation
    • Globalization and Backtracking Strategies
    • Search-Based Algorithms
  • Numerical Methods for Partial Differential Equations (15%)

Course Instructor: Jeff Borggaard

Regular office hours will be held in McBryde 528, times will be arranged at the first class meeting. Additional meeting times can be arranged by e-mail.

Course Resources

Lecture Notes and Selected Reading Material will be placed on reserve in the library.

This course will be managed using the Virginia Tech Scholar site.

Recent Course Contract

Math 5434 - Principles and Techniques of Applied Mathematics - Fall 2013


Jeff Borggaard, regular office hours will be held in McBryde 528. Students are invited to e-mail me at ( to arrange an appointment.


Lecture notes and selected reading material will be provided on-line, placed on reserve in the library, and referenced by links.

Evaluation and Grading

Regular homework assignments constitute 25% of the grade. An in-class exam will be worth 25% and the remainder of the course evaluation will be based on programming projects..

Honor Code

You are encouraged to discuss regular homework assignments with other members of the class, however any submitted write-up and code to be graded should be your work alone. All exams (in-class or takehome) must be worked on independently.

Failure to follow these restrictions, and giving or receiving unauthorized aid or assistance on homework, in-class exams on the take-home final are Virginia Tech Honor System violations and cases will be filed.