# Numerical Analysis

Cengage Learning, 2011 - Numerical analysis - 872 pages
This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.

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Solve the following equation using Newton-Raphson method:
𝑥2−4𝑥2+4=0

### Contents

 Mathematical Preliminaries and Error Analysis 1 Solutions of Equations in One Variable 47 Interpolation and Polynomial Approximation 105 Numerical Differentiation and Integration 173 InitialValue Problems for Ordinary Differential Equations 259 Direct Methods for Solving Linear Systems 357 Iterative Techniques in Matrix Algebra 431 Approximation Theory 497
 Approximating Eigenvalues 561 Numerical Solutions of Nonlinear Systems of Equations 629 BoundaryValue Problems for Ordinary Differential Equations 671 Numerical Solutions to Partial Differential Equations 713 Bibliography 763 Answers for Selected Exercises 773 Index 863 Copyright