An Introduction to Approximation Theory

Lectures for Fall 2009

1. Introduction to Concepts of Approximation Theory

2. Space of Continuous Functions, Polynomials and Bernstein Polynomial

3. Modulus of Continuity and Degree of Convergence

4. Classical Fourier Series and Jackson's Theorem for Trigonometric Polynomials

5. Existence/Uniqueness and Characterization of Best Uniform Approximants

6. Characterization of Best Uniform Approximants - Case of Algebraic Polynomials

7. Characterization of Best Uniform Approximants - Chebyshev Systems

8. Hilbert Spaces and General Fourier Series

9. Classical Fourier Series

10. Jackson's Theorem for Trigonometric Polynomials

11. The Bernstein and Markov's Inequalities

12. Radial Basis Functions and Multivariate Interpolation