Math 620 - Numerical Analysis

Basic Information

• Matthias K. Gobbert, Math/Psyc 416, (410) 455-2404, gobbert@umbc.edu,
  office hours: TuTh 02:30-03:30 or by appointment
• Classes: Math/Psyc 105, TuTh 04:00-05:15; see the detailed schedule for more information.
• Prerequisites: Math 221, Math 225, Math 251, Math 301, CMSC 201, or instructor approval
• Copies of the following books are on reserve in the library. These books are highly recommended as reference, but are not required. The intention is to cover the material of the course sufficiently well by the lectures, possibly complemented by specific reading assignments, for which you can use the reserve copies in the library.
  • Recommended textbook: Kendall E. Atkinson, An Introduction to Numerical Analysis, second edition, Wiley, 1989. Associated webpage: http://www.math.uiowa.edu/~atkinson/keabooks.html
    An analytical introduction to the subject, comprehensive and timeless.
  • Recommended book on Matlab: Desmond J. Higham and Nicholas J. Higham, Matlab Guide, third edition, SIAM, 2017. Webpage of the book including list of errors.
    Matlab's documentation is excellent, but along with its functionality has reached a scale that requires a lot of sophistication to fully understand. Moreover, there is a definite role for a book that is organized by chapter on topics such as all types of functions (inline, anonymous, etc.), efficient Matlab programming (vectorization, pre-allocation, etc.), Tips and Tricks, and more.
• Grading rule:
  

  Homework and Quizzes	Participation	Midterm Exam	Final Exam or Project
  30%	10%	30%	30%

  • The homework assignments will be posted in the Blackboard site of our course; see below. The detailed schedule indicates the due date of each homework. The homework includes the computer assignments that are vital to understanding the course material. A late assignment accrues a deduction of up to 10% of the possible score for each day late until my receiving it; I reserve the right to exclude any problem from scoring on late homework, for instance, if we discuss it in class. The quizzes will generally be unannounced and brief and will include the use of learning groups formed by the instructor. For instance, they may be designed to initiate class discussion or to give me feedback on your learning. They may be technical or non-technical in nature.
  • The graded participation component rewards your professional behavior and active involvement in all aspects of the course. Examples of expected professional behavior include attending class regularly, reading assigned material when requested, cooperating with formal issues such as submitting requested material on time, and participating constructively in class, specifically in group work.
  • The midterm and final exams are traditional in-class exams. To help you focus on what is relevant, they are closed-book and closed-notes, but you should bring a scientific calculator. See the detailed schedule for the dates of the exams.
  • It is increasingly important at this point in your education to learn how to work on a larger project on your own (with guidance by the instructor) and to present your results in the form of a professional-grade type-set report. To allow interested students to develop the necessary skills, you may choose to replace the final exam by a project; since I assume here that this is a new experience for you and not suitable for all students, you must talk to me for approval. I want to mention that a class project is a great way to start on a research project, in case that is something you are interested in.
  Additional details or changes will be announced as necessary. See also general rules and procedures for more information.
• Blackboard is a course management system that allows for posting and communicating among registered participants of a course. We will actively use only the "Course Materials" area and the "Discussion Board" of our course in Blackboard. I will post class summaries and PDF files of the lecture notes as well as other material including the homework assignments in the "Course Materials" area. The "Discussion Board" is for all contents questions; for efficiency in communications, I cannot reply to e-mails on contents-questions; please post them in the "Discussion Board". I will also use Blackboard to send e-mail to the class, which goes to your UMBC account by default. Therefore, you must either check your UMBC e-mail regularly or have the mail forwarded to an account that you check frequently.

Course Description

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 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

• understand and remember the key ideas, concepts, definitions, and theorems of the subject. Examples include computational algorithms, sources of error, convergence theorems, and implementations of these algorithms. More broadly, you should also understand the purpose of numerical analysis.
  --> This information will be discussed in the lecture. You will apply and use them on homeworks, quizzes, and tests.
• have experience using a professional software package, writing code in it, and understanding how some of its functions work. We will focus on the package Matlab in this course, which is the most popular package in mathematics and many application areas. Writing code in this context includes the requirements to deliver code in a form required, such as writing code to stated specifications, using a requested method, complying with a required function header, etc. The knowledge and skills in this item are valuable job skills, which justifies the emphasis here.
  --> This is one of the purposes of the homework and most learning will take place here.
• have some foundational experience in writing professional-grade reports in Mathematics. This is explained more in the syllabus portion on How to Report on Computer Results.
  --> This is included in the homeworks and is also one of the reasons for offering a project option.
• have experience working actively with peers in a group, both on the scale of the class and in a smaller team. Group work requiring communication for effective collaboration with peers and supervisors is a vital professional skill, and the development of professional skills including this networking is a declared learning goal of this course. Additionally, getting to know other students as part of learning groups will prove invaluable for homework and tests.
  --> The groups will be assigned by the instructor and used for group quizzes in class. Their formal evaluation is included in the participation category of the grading rule.

Other Information

• Detailed schedule
• General rules and procedures including grading guidelines
• Guidelines on how to report on computer results

• The recommended literature on my homepage
• A brief introduction to Unix/Linux at UMBC
• Introduction to Matlab at UMBC (maintained by CIRC)
• An introduction to LaTeX including a sample file and a template file for project reports.

• UMBC High Performance Computing Facility (HPCF) including general information, list of projects, publications page, and resources for users.
• Center for Interdisciplinary Research and Consulting (CIRC)

UMBC Statement of Values for Academic Integrity