Methods of Computational Math I (MATH/CS 714)

MATH/CS 714 - Methods of Computational Math I (Finite Differences)
Tuesdays & Thursdays 8:00am - 9:15am, B105 Van Vleck

Instructor:

Name	Office	Phone	E-Mail	Office Hours
James Rossmanith	505 Van Vleck	262-3852	rossmani AT math DOT wisc DOT edu	T. & Th. 2:00pm-3:00pm

Course description

Textbook

Syllabus

MATLAB Help

Python Help

Homework

Handouts

Course Description

Prerequisites:

an advanced undergraduate course in PDEs (on the level of Haberman's book on "Applied Partial Differential Equations");
an advanced undergraduate course in numerical analysis (on the level of Burden and Faires's book on "Numerical Analysis");
knowledge in a programming language (e.g., Fortran, C/C++, or MATLAB).

Math/CS 714 and Math/CS 715 are concerned with the development and the analysis of numerical methods for solving elliptic, parabolic, and hyperbolic partial differential equations (PDEs). In particular, Math/CS 714 will focus on a class of numerical schemes known as finite difference methods. For each type of PDE we will develop numerical schemes from physical and mathematical intuition, analyze these schemes, consider improvements, and discuss issues related to the impelementation these methods into computer code.

An important aspect of accurately and efficiently solving PDEs via numerical methods is the ability to solve large linear systems. Therefore, in addition to the basic numerical methods, this course will include discussions of simple iteration methods for solving large linear systems, Krylov subspace methods, and basic geometric multi-grid (time permitting). Homework assignments will involve problems on theoretical (analyzing methods) and practical (implementing methods into computer code) aspects of numerical analysis.

Textbook

R.J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, 2007. ISBN 978-0-898716-29-0.

Syllabus

Download syllabus: (PDF)

MATLAB Help

Download guide to MATLAB plotting [MSCC, University of Washington, 1996]: (PDF)
Download MATLAB tutorial: (PDF)
Go to the MATLAB Help Desk at the MathWorks site.
This allows you to search for a specific MATLAB function.

Python Help

SciPy main website: (http://www.scipy.org)
Download Python, NumPy, SciPy, Matplotlib, and IPython from Enthought: (http://enthought.com/products/epd.php)
NumPy and SciPy tutorial: (http://www.scipy.org/Tentative_NumPy_Tutorial)

Homework

Follow links in the table below to obtain a copy of the homework in Adobe Acrobat (PDF) format.

Homework Sets

Homework #1 (PDF)

Homework #2 (PDF)

Homework #3 (PDF)

Homework #4 (PDF)

Homework #5 (PDF)

Homework #6 (PDF)

Project Description (PDF)

Handouts

Finite difference example -- truncation error and round-off error (PDF)
Natural rowwise ordering example (PDF)