Math 4650/5650 - Numerical Analysis - Fall 2017
Dr. Radu C. Cascaval

 

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Course Info:

Time/Place: Monday & Wednesday, 12:15-1:30pm, OSB B213
Office Hours: Monday & Wednesday 11-12pm or by appointment (ENG 271)
Course Website: http://academics.uccs.edu/rcascava/Math4650
Email: [email protected]

Course Description

The main goal of the course is to provide a systematic introduction to numerical methods, as a first step in understanding the mathematics of computation and how it is used in solving real world problems.. The emphasis will be on the construction, analsysis and implementation of numerical algorithms and on developing numerical experience in a problem solving environment.

The lectures will cover selected sections in Chapters 4-14 of the textbook. Topics include: finding roots of functions of one variable, solving linear systems, finding eigenvalues and eigenvectors of matrices, interpolation and curve fitting, numerical differentiation and integration and solving ordinary differential equations (initial and boundary value problems) and partial differential equations. The course has a BlackBoard companion website for access to grades, various handouts, solutions to HMW exercises etc.

Textbook (required):

Numerical Analysis - by Richard Burden, Douglas Faires and Annette Burden
- Author's companion website http://sites.google.com/site/numericalanalysis1burden

Supplementary readings:

1. Scientific Computing with MATLAB and Octave, 2nd edition, by A. Quarteroni, F. Saleri, Springer 2006
(FREE* download for UCCS students on Springerlink.com, or you may also purchase a papercopy for $24.95 including S&H)
[*You must be on the campus network to be able to freely download individual chapters of the book.]

2. Numerical Computing with MATLAB, by Cleve Moler, SIAM 2004
(FREE chapter-by-chapter download - Mathworks Website)

3. A Friendly Introduction to Numerical Analysis, by B. Bradie, Prentice Hall, 2006
- Solutions to selected exercises: http://www.pcs.cnu.edu/~bbradie/textbookanswers.html
- Matlab Codes: http://www.pcs.cnu.edu/~bbradie/matlab.html

4. Numerical Methods in Scientific Computing, Vol 1, by G. Dahlquist and A. Bjorck, SIAM 2008
(selected Chapters and Appendices freely downloadable - SIAM Website)

Computer software (MATLAB)

A majority of the problems discussed in class and those assigned for homework will require the effective use of a computer. MATLAB is the software of choice during our class; no prior experience with MATLAB is expected. The best way to learn how to use MATLAB is through examples; some will be given in class, others will be suggested outside class. Although mastering MATLAB is NOT one of our goals in this class, you are expected to be able to read and understand the codes I provide and ccreate some basic ones of your own.

MATLAB is freely accessible to UCCS students for install on their own computers. It is also available in all computer labs accross campus (including 233 and the Library), thanks to a campus-wide site license. Instructions to get access MATLAB are available at this page.

Homework:

Weekly sets of homework problems from the textbook and other sources will be assigned, with due date on Wednesdays, unless otherwise specified. No late homework will be accepted or graded. For Math 5650 credit, students will have a project to work on. Although I encourage discussions outside of classroom on the topics covered in class and on exercises assigned for HMW, individual solutions to homework problems are expected from each student.

Please note, many of the HMW problems require a blend of theoretical analysis and computer implementation. Team work on the computer part is allowed, however individual work is required to be turned in. Dishonest use of other people's work or ideas will be severely punished, up to and including disciplinary actions.

Exams:

There will be 2 midterm Exams during the semester and a comprehensive Final Exam, as follows

Exam 1: Wednesday, Oct 11
Exam 2: Wednesday, Nov 15
Final Exam: Wednesday, Dec 13, 10:20am-12:20pm

There will be no make up exams so please mark your calendars! If a student informs me well before the exam date about absolutely having to miss an upcoming exam AND provides acceptable written verification in support of the request, then the final exam score will be used to replace that particular exam. If any of the above conditions is not satisfied, the student will get a zero on the missed exam. The above procedure may only be applied once. The Final Exam cannot be missed under any circumstances.

Grading:

The course grade will be the higher of the two derived according to the following schemes: Scheme 1 = homework (30%), the two exams (20% each) and the final exam (30%); Scheme II = homework (30%), the best of two exams (30%) and final (40%). The final scores will be 'curved' to reflect the class distribution. Each student will receive a letter grade based on his/her relative standing in the class. Although attendance and participation do not formally enter the above computation, they will be taken into account every time one's score falls close to the cut-off value for a particular letter grade. At the same time you may be assured that if your score is at least 90% (or 80%,70%), then your letter grade will be at least A (or B, C respectively).

Other policies:

To make the most of your class, you are required to attend every class session. Students should notify (in advance) the instructor if they need to miss more than one session. Supporting documentation may be required. Drop dates: Please seek counseling from the Dean's office before dropping any course and note the following important dates: Sept 7, 2017 – last day to drop and receive a full tuition refund; Oct 27, 2017– last day to drop without special permission from the Dean.

Academic Dishonesty:

Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the course instructor.

Disability Services:

Students with disabilities should contact the Office of Disability Services (Main Hall 105, 255-3354) and also notify the instructor of any special needs. They should provide a letter of certification from the Office of Disability Services within the first 2 weeks of classes.