Theoretical Numerical Analysis

PrefacePreliminariesChapter 1. Interpolation and Quadrature 1.1. Hermite Interpolation 1.2. Lagrange Interpolation and Newton-Cotes Quadrature 1.3. Orthogonal Polynomials and Gaussian Quadrature 1.4. Nonanalytic Interpolation and Associated Quadrature Exercises Computer Problems NotesChapter 2. Approximation 2.1. Degree of Approximation by Polynomials 2.2. Approximation by Interpolation 2.3. Chebyshev Approximation 2.4. An Algorithm for Chebyshev Approximation Appendix Exercises Computer Problems NotesChapter 3. Ordinary Differential Equations 3.1. The Initial Value Problem 3.2. An Inhomogeneous Boundary Value Problem 3.3. A Homogeneous Boundary Value Problem Exercises Computer Problems NotesChapter 4. Solution of Equations 4.1. Matrix Inversion by Triangular Decomposition 4.2. The Matrix Eigenvalue Problem 4.3. Linear Iterative Methods 4.4. Iterative Methods for Nonlinear Systems Exercises Computer Problem NotesChapter 5. Partial Differential Equations 5.1. First Order Systems 5.2. The Heat Equation 5.3. Stability 5.4. The Maximum Principle Exercises NotesReferencesAdditional ReadingAuthor IndexSubject Index