MATH 708
Meeting times: TTh 2:00  3:15 PM at LeConte (LC) 121.
Instructor: Dr. Peter G. Binev http://www.math.sc.edu/~binev/
email: binev@math.sc.edu)
phones: 5766269 (at LC 425) or 5766304 (at SUM 206H)
Office hours: TTH 1:00  2:00 PM at LeConte 425 or by appointment.
Prerequisites: Math 554 or equivalent upper level undergraduate course in Real Analysis.
Learning Outcomes: At the end of this course students will be able to read, interpret, use vocabulary, symbolism, and basic definitions and theorems from Numerical Analysis. The students will be able to use facts, formulas, and techniques learned in this course to apply algorithms and theorems to find numerical solutions and bounds on their errors to various types of problems including root finding, polynomial interpolation and approximation, fast Fourier transform, numerical differentiation and integration, and spline approximation.
Attendance: Regular class attendance is important. A grade penalty will be applied to any student missing three or more classes (10%) during the semester. The "10 percent rule" stated above applies to both excused and unexcused absences. Students who anticipate potential excessive absences due to participation in permissible events as described in the USC Academic Bulletins (http://www.sc.edu/bulletin/ugrad/acadregs.html#class atten.) should receive prior approval from the instructor to potentially avoid such penalty.
Cell Phones: All cell phones must be turned off during the class.
Homework: A few homework problems will be assigned each class. Be sure to solve and write these problems before the next class. Some solutions will be collected and graded. Particular homework problems will be discussed and/or presented by a student in class. Both the written solutions and the participation in the discussions will be taken into account in forming the homework grade.
Projects: Every student has to choose a project motivated by the computational or theoretical problems discussed in the course. Several possible themes for the projects will be suggested by the instructor in the length of the course. The project in a form of a poster, slides/presentation, or a short paper should be submitted on or before November 23, 2010.
Discussions: The homework and the projects will be discussed in class. The participation in the discussions will be taken into account as part of the homework grade.
Exams: There will be two exams both in a form of a test. The tentative date for the midterm exam is September 28, 2010. The tentative date for the second exam is November 4, 2010. The problems on the tests will be similar to the ones from the homework and the discussions in class.
Final Exam: The final exam in a form of a test will take place on Thursday, December 8 at 2:00 PM.
Grading: The final grade will be determined from the homework (20%), the exams (30%), the project (25%), and the final (25%).
Academic Dishonesty: Cheating and plagiarism will not be allowed. The University of South Carolina has clearly articulated its policy governing academic integrity and students are encouraged to carefully review the policy on the Honor Code in the Carolina Community (see http://www.housing.sc.edu/academicintegrity/policy.html).
ADA: If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.
Important Dates:
September 28 First Exam
November 4 Second Exam
November 23 Deadline to submit the projects
December 8 Final Exam at 2:00 PM
Preliminary Schedule of Classes
Date 
Chapter 
Subject 
Aug. 19 
handouts 
Introduction and Computational Errors 
Aug. 24 
1 
Nonlinear Equations 
Aug. 26 
1 
Nonlinear Equations 
Aug. 31 
4 
Nonlinear Equations and Systems 
Sept. 2 
6 
Polynomial Interpolation 
Sept. 7 
www / help 
Matlab 
Sept. 9 
www / help 
Matlab 
Sept. 14 
handouts 
Divided Differences 
Sept. 16 
6 
Polynomial Interpolation 
Sept. 21 
11 
Spline Functions 
Sept. 23 

Review 
Sept. 28 
EXAM 

Sept. 30 
handouts 
Bsplines 
Oct. 5 
handouts 
Computer Aided Geometric Design 
Oct. 7 
8 
Polynomial Approximation in the Infinity Norm 
Oct. 12 
8 
Polynomial Approximation in the Infinity Norm 
Oct. 19 
9 
Polynomial Approximation in Hilbert Space 
Oct. 21 
9 
Polynomial Approximation in L_{2} norm 
Oct. 26 
handouts 
Trigonometric Polynomials and Fast Fourier Transform 
Oct. 28 
handouts 
Fast Fourier Transform 
Nov. 2 

Review 
Nov. 4 
EXAM 

Nov. 9 
6 
Numerical Differentiation 
Nov. 11 
7 
Numerical Integration 
Nov. 16 
7 
Numerical Integration 
Nov. 18 
10 
Numerical Integration 
Nov. 23 
10 
Numerical Integration 
Nov. 30 

Review / Presentations 
Dec. 2 

Review 



Dec. 8 
2:00 p.m. 
Final Exam 