Math 578 > General information

General information

Catalog description
Development, analysis and effective use of numerical methods to solve problems arising in applications. Topics include direct and iterative methods for the solution of linear equations (including preconditioning), eigenvalue problems, interpolation, approximation, quadrature, solution of nonlinear systems.

Topics to be covered
Direct methods for linear systems: Gaussian elimination, LU factorization and variants, triangular matrices, QR factorization, conditioning and stability
Iterative methods for linear systems: Jacobi, Gauss-Seidel, SOR, GMRES, conjugate gradients, preconditioning
Eigenproblems: reduction to Hessenberg or tridiagonal form, QR algorithm, Jacobi method
Nonlinear systems: fixed point iteration, Newton-Raphson and variants
Least squares problems: normal equations, QR factorization, singular value decomposition
Approximation of functions: interpolation, least squares approximation, uniform approximation, use of polynomial and trigonometric functions, numerical integration (i.e., quadrature)

MATH 247 or MATH 251; and MATH 387; or permission of the instructor.

Authors: Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri
Title: Numerical mathematics
Series: Texts in Applied Mathematics 37
Edition: Any. Publisher: Springer
Electronic version: Available on SpringerLink (e.g. from McGill campus)

Recommended reading
  • Robert Plato. Concise numerical mathematics. GSM 57. AMS
  • Lloyd Nick Trefethen and David Bau III. Numerical linear algebra. SIAM
  • Germund Dahlquist and Ake Bjorck. Numerical methods. Dover
  • Kendall Atkinson and Weimin Han. Theoretical numerical analysis. TAM 39. Springer
  • Eugene Isaacson and Herbert Bishop Keller. Analysis of numerical methods. Dover
  • Online resources
    Matlab is the official mathematical software and programming tool of the class.

    WF 11:35am-12:55am, Burnside Hall 1205

    Dr. Gantumur Tsogtgerel
    Office: Burnside Hall 1123. Phone: (514) 398-2510. Email: gantumur -at-
    Office hours: WF 2-4pm, or just stop by.

    Homework Assignments
    Both analytical and computational. Assigned and graded roughly every two weeks.
    • For computational problems, print out and submit the code that you modified or created (usually the m-file) and the main result (e.g., outputs in text and/or graphics format) only.

    There will be one midterm exam in early October, and a final exam in December. The final exam will be cumulative.

    The final course grade will be the best of the following two weighted averages:
  • analytic homework 25%, computer homework 25%, the midterm exam 20%, and the final exam 30%;
  • analytic homework 25%, computer homework 25%, and the final exam 50%.

    MATH 578: Numerical Analysis 1 Fall 2009