A Graduate Introduction to Numerical Methods

​Computer Arithmetic & Fundamental Concepts of Computation

Polynomials and Series

Rootfinding and Function Evaluation

Solving \(\mathbf{Ax} = \mathbf{b}\)

Solving \(\mathbf{Ax} =\lambda \mathbf{x}\)

Structured Linear Systems

Iterative Methods

Polynomial and Rational Interpolation

The Discrete Fourier Transform

Numerical Integration

Numerical Differentiation and Finite Differences

Numerical Solution of ODEs

Numerical Methods for ODEs

Numerical Solutions of Boundary Value Problems

Numerical Solution of Delay DEs

Numerical Solution of PDEs

Afterword

Appendices