COURSE SYLLABUS Course Number: MATH6180 Course Title: INTRODUCTION TO APPROXIMATION THEORY Credit Hours: 3 Prerequisites: MATH 0265 or departmental approval Corequisite: Course Objectives: To present to the interested undergraduate student the basic methods of approximation by polynomial, trigonometric, and spline functions. Course Content: Uniform Approximation: Uniform Approximation by polynomials and trigonometric Polynomials; the Weierstrass theorem and Bernstein polynomial approximation (5 hrs); Jackson's theorems (5 hrs). Characterization of best approximations (4 hrs). Approximation on a finite set of points (2 hrs). Computational methods (2 hrs). Least-squares approximation: Approximation on an interval; the Jacobi polynomials (4 hrs). Approximation on a finite set of points (2 hrs). Effectiveness as a uniform approximation (2 hrs). Polynomial and spline interpolation: General results (3 hrs). The size of the Lebesgue constants (3 hrs). Interpolating polynomials as least-squares approximations (2 hr). Interpolation and approximation by splines (5 hrs). Possible textbooks: T. J. Rivlin, An introduction yo the approximation of functions, Dover, NewYork, 1969. E. W. Cheney, Introduction to Approximation Theory, second edition, AMS/Chelsea, 1982. Grading and Evaluation Procedures: Quizzes, tests, midterm exam, final exam. Other methods of evaluation are used at the discretion of the instructor. Statement related to policies on unannounced quizzes and class attendance and participation: Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester.