Numerical Analysis with Algorithms and Programming

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering.

Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica^® programs, the book includes the standard algorithms for numerical computation:

• Root finding for nonlinear equations
• Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines
• The solution of systems of linear equations and triangularization
• Approximation of functions and least square approximation
• Numerical differentiation and divided differences
• Numerical quadrature and integration
• Numerical solutions of ordinary differential equations (ODEs) and boundary value problems
• Numerical solution of partial differential equations (PDEs)

The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.

Table of Contents

Chapter 1: Errors in Numerical Computations
Chapter 2: Numerical Solutions of Algebraic and Transcendental Equations
Chapter 3: Interpolation
Chapter 4: Numerical Differentiation
Chapter 5: Numerical Integration
Chapter 6: Numerical Solution of System of Linear Algebraic Equations
Chapter 7: Numerical Solutions of Ordinary Differential Equations
Chapter 8: Matrix Eigenvalue Problem
Chapter 9: Approximation of Functions
Chapter 10: Numerical Solutions of Partial Differential Equations
Chapter 11: An Introduction to the Finite Element Method