Math 5465

Numerical Analysis

This course is managed under the Canvas course management system. Information is provided here for convenience, but the canvas site should be consulted for any official course policy.
Course Description

From Catalog:

A survey of the construction, analysis, and implementation of numerical algorithms in linear algebra, nonlinear equations and optimization, approximation by polynomials, quadrature, and ordinary differential equations. High-level programming language required.

The first semester of this course emphasizes numerical linear algebra including forward and backward error analysis (stability and conditioning), numerous matrix factorizations including the singular value deccomposition (SVD), QR, LU, Cholesky, etc. In addition, iterative algorithms for linear systems and eigenvalue problems are covered. A list of topics includes:

  • Working in Finite Precision Arithmetic
  • Error Analysis and Numerical Stability
  • Matrix Decompositions (Analysis of Algorithms)
  • Iterative Algorithms
  • Introduction to Nonlinear Equations

In the second semester (5466), we will discuss:

  • Approximation Theory
  • Nonlinear Equations and Optimization
  • Numerical Methods for ODEs
  • Survey of Topics for Further Study

Course Instructor: Jeff Borggaard

Regular office hours will be held in McBryde 528, Monday afternoons from 1-3 PM. Additional meeting times can be arranged by e-mail.

Course Resources

Selected reading material will be placed on reserve in the library.

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

Course Contract Highlights

Math 5465 - Numerical Analysis - Fall 2017


Jeff Borggaard, regular office hours will be held in McBryde 528 from 1-3 PM. Students are invited to e-mail me at ( to arrange an appointment.


Lectures will be held MWF from 11:15-12:05 in 305 Patton Hall.


Numerical Linear Algebra, Trefethen and Bau, SIAM (link to SIAM page) as well as additional material.

Evaluation and Grading

Regular homework assignments constitute 50% of the grade. An in-class exam and in-class/take-home final exam will be worth 25% each.

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 and 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.