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Full Description
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.
Contents
Errors in Numerical Computations. Numerical Solutions of Algebraic and Transcendental Equations. Interpolation. Numerical Differentiation. Numerical Integration. Numerical Solution of System of Linear Algebraic Equations. Numerical Solutions of Ordinary Differential Equations. Matrix Eigenvalue Problem. Approximation of Functions. Numerical Solutions of Partial Differential Equations. An Introduction to the Finite Element Method. Bibliography. Answers. Index.
