Math 620 - Numerical Analysis

Fall 2020 - Syllabus - Matthias K. Gobbert

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Basic Information

Course Description

Numerical Analysis are 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, approximation theory and orthogonal polynomials, the solution of systems of non-linear 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 or equivalently the free and nearly fully compatible package Octave as platform of choice, because they are very popular packages and knowing them thoroughly is itself a marketable skill. For both packages, you can read its expansive and well-written documentation or you may consider the book recommended above. For hands-on training in Matlab and Octave, 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

Note on Recordings and Their Publication

This class is being audio-visually recorded so students who cannot attend a particular session and wish to review material can access the full content. This recording will include students' images, profile images, and spoken words, if their camera is engaged and their microphone is live. Students who do not consent to have their profile or video image recorded should keep their camera off and not use a profile image. Likewise, students who do not consent to have their voice recorded should keep their mute button activated and participate exclusively through alternative formats such as email or the chat feature (where available).

UMBC Statement of Values for Academic Integrity

Academic integrity is an important value at UMBC. 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. Consult the the UMBC webpage on Academic Integtrity at for the UMBC Undergraduate Student Academic Conduct Policy for undergraduate students and the UMBC Graduate School's Policy and Procedures for Student Academic Misconduct for graduate students.

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This page version 1.5, August 2020.