Math 441 - Introduction to Numerical Analysis

Fall 2015 - Syllabus Matthias K. Gobbert

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Basic Information

Course Description

Numerical Analysis is concerned with the approximation of mathematical objects, the analysis of the errors incurred in this approximation, and the development and implementation of computer algorithms for the computation of these approximations. The approximations take various forms including the approximation of a function by a series with finitely many terms or the approximation of a derivative by a finite difference. These approximations incur numerical error, in the examples above known as truncation error and discretization error, respectively.

The methods covered include polynomial interpolation, numerical differentiation and integration, the solution of non-linear systems of equations, and an introduction to numerical methods for ordinary differential equations. Additionally, we will discuss Gaussian elimination for the solution of systems of linear equations and other selected topics such as the representation of real numbers in computers according to the IEEE-standard for floating-point numbers.

This course will also include computational work to gain practical experience with the numerical methods discussed. I recommend the professional software package Matlab as platform of choice, because it is a very popular package and knowing it thoroughly is itself a marketable skill. To read about Matlab, you can read its expansive and well-written documentation or you may consider the book recommended above. For hands-on training in Matlab, you can consider the 2-credit class Math 426 on Matlab or for a brief initial overview the software workshops offered by CIRC.

Learning Goals

By the end of this course, you should:

Other Information

UMBC Academic Integrity Policy

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage, the UMBC Undergraduate Student Academic Conduct Policy (PDF) for undergraduate students, or the University of Maryland Graduate School, Baltimore (UMGSB) Policy and Procedures for Student Academic Misconduct (PDF) for graduate students.

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This page version 2.4, September 2015.