# 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)

**Prerequisites**

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

**Textbook**

*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

**Software**

Matlab is the official mathematical software and programming tool of the class.

**Lectures**

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

**Instructor**

Dr. Gantumur Tsogtgerel

*Office*: Burnside Hall 1123.
*Phone*: (514) 398-2510.
*Email*: gantumur -at- math.mcgill.ca

*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.*

**Exams**

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

**Grading**

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%.