1. Introduction
2. Chebyshev Points and Interpolants
3. Chebyshev Polynomials and Series
4. Interpolants, Projections, and Aliasing
5. Barycentric Interpolation Formula
6. Weierstrass Approximation Theorem
7. Convergence for Differentiable Functions
8. Convergence for Analytic Functions
9. Gibbs Phenomenon
10. Best Approximation
11. Hermite Integral Formula
12. Potential Theory and Approximation
13. Equispaced Points, Runge Phenomenon
14. Discussion of High-Order Interpolation
15. Lebesgue Constants
16. Best and Near-Best
17. Orthogonal Polynomials
18. Polynomial Roots and Colleague Matrices
19. Clenshaw-Curtis and Gauss Quadrature
20. Carathéodory-Fejér Approximation
21. Spectral Methods
22. Linear Approximation: Beyond Polynomials
23. Nonlinear Approximation: Why Rational Functions
24. Rational Best Approximation
25. Two Famous Problems
26. Rational Interpolation and Linearized Least-Squares
27. Padé Approximation
28. Analytic Continuation and Convergence Acceleration
Appendix: Six Myths of Polynomial Interpolation and Quadrature
References
Index

Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It is aimed at advanced undergraduates and graduate students across all of applied mathematics