Part I: Approximating Functions, Derivatives and Integrals. 1. Spectral Approximation.
2. Algorithms For Periodic Functions.
3. Algorithms For Non-Periodic Functions.
Part II: Approximating Solutions of PDEs. 4. Survey of Spectral Approximations.
5. Spectral Approximation on the Square.
6. Transformation Methods from Square to Non-Square Geometries.
7. Spectral Methods in Non-Square Geometries.
8. Spectral Element Methods.
A: Miscellaneous Algorithms.
B. Floating Point Arithmetic.
C. Basic Linear Algebra Subroutines (BLAS).
D. Linear Solvers.
E. Data Structures.