Book:Walter Gautschi/Numerical Analysis: An Introduction

Subject Matter

 * Numerical Analysis

Contents

 * Preface


 * Chapter 0. Prologue


 * Chapter 1. Machine Arithmetic and Related Matters
 * 1. Real Numbers, Machine Numbers, and Rounding
 * 2. Machine Arithmetic
 * 3. The Condition of a Problem
 * 4. The Condition of an Algorithm
 * 5. Computer Solution of a Problem; Overall Error
 * Notes to Chapter 1
 * Exercises and Machine Assignments to Chapter 1


 * Chapter 2. Approximation and Interpolation
 * 1. Least Squares Approximation
 * 2. Polynomial Interpolation
 * 3. Approximation and Interpolation by Spline Functions
 * Notes to Chapter 2
 * Exercises and Machine Assignments to Chapter 2


 * Chapter 3. Numerical Differentiation and Integration
 * 1. Numerical Differentiation
 * 2. Numerical Integration
 * Notes to Chapter 3
 * Exercises and Machine Assignments to Chapter 3


 * Chapter 4. Nonlinear Equations
 * 1. Examples
 * 2. Iteration, Convergence, and Efficiency
 * 3. The Methods of Bisection and Sturm Sequences
 * 4. Method of False Position
 * 5. Secant Method
 * 6. Newton's Method
 * 7. Fixed Point Iteration
 * 8. Algebraic Equations
 * 9. Systems of Nonlinear Equations
 * Notes to Chapter 4
 * Exercises and Machine Assignments to Chapter 4


 * Chapter 5. Initial Value Problems for ODEs - One-Step Methods
 * 1. Local Description of One-Step Methods
 * 2. Examples of One-Step Methods
 * 3. Global Description of One-Step Methods
 * 4. Error Monitoring and Step Control
 * 5. Stiff Problems
 * Notes to Chapter 5
 * Exercises and Machine Assignments to Chapter 5


 * Chapter 6. Initial Value Problems for ODEs - Multistep Methods
 * 1. Local Description of Multistep Methods
 * 2. Examples of Multistep Methods
 * 3. Global Description of Multistep Methods
 * 4. Analytic Theory of Order and Stability
 * 5. Stiff Problems
 * Notes to Chapter 6
 * Exercises and Machine Assignments to Chapter 6


 * Chapter 7. Two-Point Boundary Value Problems for ODEs
 * 1. Existence and Uniqueness
 * 2. Initial Value Techniques
 * 3. Finite Difference Methods
 * 4. Variational Methods
 * Notes to Chapter 7
 * Exercises and Machine Assignments to Chapter 7


 * References


 * Subject Index