Course information

Instructor

  • Prof. Randall LeVeque
    • Office: Lewis 328
    • netid for email: rjl
    • Office hours in Lewis 328: Monday 11:00am-12:00pm and Tuesday 4:00-5:00pm
    • Office hours online: Monday 5:00-6:00pm and Tuesday 7:00-8:00am (Pacific) (see Canvas for connection information)

TA

  • Scott Moe
    • netid for email: smoe
    • Office hours in Lewis 128: Monday 4:30-5:30pm and Friday 11:00am-12:00pm
    • Office hours online: Monday 12:00-1:00pm and Friday 5:00-6:00pm (Pacific) (see Canvas for connection information)

Lectures

  • MWF 2:30 - 3:20 pm in Loew 216

Canvas Page

Registered students should have access to the Canvas course page, where you will find links to videos of lectures, the discussion board, and additional information about homeworks and exams.

Assignments

See Homework and exams for more information and due dates.

Course Description

This course is an introductory graduate level course in numerical methods designed to give engineering, mathematics, and science students the expertise necessary to understand and use computational methods for solving scientific problems. The emphasis is on methods for linear algebra problems (direct methods for linear systems, linear least squares problems, and algebraic eigenvalue problems).

This course is the first in a series of three numerical methods courses. Amath 585 treats boundary value problems (ODEs and PDEs) and iterative methods for their numerical solution. Amath 586 treats initial value problems (ODEs), parabolic and hyperbolic PDEs and methods for their numerical solution. This is a five (5) credit course.

Prerequisites

  • Some Computing Programming (Matlab, Python, R, Fortran, or C)
  • Linear Algebra (e.g. MATH 308, AMATH 352, or equivalent)

Computer Software

Please use either Matlab or Python. Examples will be presented in both languages in some cases.

See Software for the course for more about your options.

Textbook

Note that you can purchase it direct from SIAM with a substantial discount if you are a SIAM member, and that student membership is free!

See Some other references for some other resources you might find useful.

Topics to be covered

We will cover much of parts I through V of Trefethen and Bau, Numerical Linear Algebra, along with some supplementary material.

In particular:

  • Review of basic linear algebra in finite dimensional spaces, including both \(R^n\) and also function spaces.
  • Linear independence, bases, norms, matrix factorization, etc.
  • Orthogonality and the Singular Value Decomposition (SVD).
  • Least squares problems: QR factorizations, Gram-Schmidt, Householder transformations.
  • Conditioning of problems and stability of algorithms.
  • Linear systems of equations: Gaussian elimination and LU factorizations.
  • The eigenvalue problem: the power method and QR algorithms, relation to SVD.
  • Various applications of the above algorithms will also be considered.

Grading

Homework: 50%, midterm exam: 25%, final exam: 25%. There will be 5 homework assignments. See Homework and exams for more information and due dates.