This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers’ intuition, and demonstrate the subject’s practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden’s NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.

Half Title

Title

Statement

Copyright

Dedication

Contents

Preface

Ch 1: Mathematical Preliminaries and Error Analysis

Ch 1: Introduction

1.1: Review of Calculus

Exercise Set 1.1

1.2: Round-off Errors and Computer Arithmetic

Exercise Set 1.2

1.3: Algorithms and Convergence

Exercise Set 1.3

1.4: Numerical Software

Ch 1: Key Concepts

Ch 1: Chapter Review

Ch 2: Solutions of Equations in One Variable

Ch 2: Introduction

2.1: The Bisection Method

Exercise Set 2.1

2.2: Fixed-Point Iteration

Exercise Set 2.2

2.3: Newtonâs Method and Its Extensions

Exercise Set 2.3

2.4: Error Analysis for Iterative Methods

Exercise Set 2.4

2.5: Accelerating Convergence

Exercise Set 2.5

2.6: Zeros of Polynomials and MĂźllerâs Method

Exercise Set 2.6

2.7: Numerical Software and Chapter Review

Ch 2: Key Concepts

Ch 2: Chapter Review

Ch 3: Interpolation and Polynomial Approximation

Ch 3: Introduction

3.1: Interpolation and the Lagrange Polynomial

Exercise Set 3.1

3.2: Data Approximation and Nevilleâs Method

Exercise Set 3.2

3.3: Divided Differences

Exercise Set 3.3

3.4: Hermite Interpolation

Exercise Set 3.4

3.5: Cubic Spline Interpolation

Exercise Set 3.5

3.6: Parametric Curves

Exercise Set 3.6

3.7: Numerical Software and Chapter Review

Ch 3: Key Concepts

Ch 3: Chapter Review

Ch 4: Numerical Differentiation and Integration

Ch 4: Introduction

4.1: Numerical Differentiation

Exercise Set 4.1

4.2: Richardsonâs Extrapolation

Exercise Set 4.2

4.3: Elements of Numerical Integration

Exercise Set 4.3

4.4: Composite Numerical Integration

Exercise Set 4.4

4.5: Romberg Integration

Exercise Set 4.5

4.6: Adaptive Quadrature Methods

Exercise Set 4.6

4.7: Gaussian Quadrature

Exercise Set 4.7

4.8: Multiple Integrals

Exercise Set 4.8

4.9: Improper Integrals

Exercise Set 4.9

4.10: Numerical Software and Chapter Review

Ch 4: Key Concepts

Ch 4: Chapter Review

Ch 5: Initial-Value Problems for Ordinary Differential Equations

Ch 5: Introduction

5.1: The Elementary Theory of Initial-Value Problems

Exercise Set 5.1

5.2: Eulerâs Method

Exercise Set 5.2

5.3: Higher-Order Taylor Methods

Exercise Set 5.3

5.4: Runge-Kutta Methods

Exercise Set 5.4

5.5: Error Control and the Runge-Kutta-Fehlberg Method

Exercise Set 5.5

5.6: Multistep Methods

Exercise Set 5.6

5.7: Variable Step-Size Multistep Methods

Exercise Set 5.7

5.8: Extrapolation Methods

Exercise Set 5.8

5.9: Higher-Order Equations and Systems of Differential Equations

Exercise Set 5.9

5.10: Stability

Exercise Set 5.10

5.11: Stiff Differential Equations

Exercise Set 5.11

5.12: Numerical Software

Ch 5: Key Concepts

Ch 5: Chapter Review

Ch 6: Direct Methods for Solving Linear Systems

Ch 6: Introduction

6.1: Linear Systems of Equations

Exercise Set 6.1

6.2: Pivoting Strategies

Exercise Set 6.2

6.3: Linear Algebra and Matrix Inversion

Exercise Set 6.3

6.4: The Determinant of a Matrix

Exercise Set 6.4

6.5: Matrix Factorization

Exercise Set 6.5

6.6: Special Types of Matrices

Exercise Set 6.6

6.7: Numerical Software

Ch 6: Key Concepts

Ch 6: Chapter Review

Ch 7: Iterative Techniques in Matrix Algebra

Ch 7: Introduction

7.1: Norms of Vectors and Matrices

Exercise Set 7.1

7.2: Eigenvalues and Eigenvectors

Exercise Set 7.2

7.3: The Jacobi and Gauss-Siedel Iterative Techniques

Exercise Set 7.3

7.4: Relaxation Techniques for Solving Linear Systems

Exercise Set 7.4

7.5: Error Bounds and Iterative Refinement

Exercise Set 7.5

7.6: The Conjugate Gradient Method

Exercise Set 7.6

7.7: Numerical Software

Ch 7: Key Concepts

Ch 7: Chapter Review

Ch 8: Approximation Theory

Ch 8: Introduction

8.1: Discrete Least Squares Approximation

Exercise Set 8.1

8.2: Orthogonal Polynomials and Least Squares Approximation

Exercise Set 8.2

8.3: Chebyshev Polynomials and Economization of Power Series

Exercise Set 8.3

8.4: Rational Function Approximation

Exercise Set 8.4

8.5: Trigonometric Polynomial Approximation

Exercise Set 8.5

8.6: Fast Fourier Transforms

Exercise Set 8.6

8.7: Numerical Software

Ch 8: Key Concepts

Ch 8: Chapter Review

Ch 9: Approximating Eigenvalues

Ch 9: Introduction

9.1: Linear Algebra and Eigenvalues

Exercise Set 9.1

9.2: Orthogonal Matrices and Similarity Transformations

Exercise Set 9.2

9.3: The Power Method

Exercise Set 9.3

9.4: Householderâs Method

Exercise Set 9.4

9.5: The QR Algorithm

Exercise Set 9.5

9.6: Singular Value Decomposition

Exercise Set 9.6

9.7: Numerical Software

Ch 9: Key Concepts

Ch 9: Chapter Review

Ch 10: Numerical Solutions of Nonlinear Systems of Equations

Ch 10: Introduction

10.1: Fixed Points for Functions of Several Variables

Exercise Set 10.1

10.2: Newtonâs Method

Exercise Set 10.2

10.3: Quasi-Newton Methods

Exercise Set 10.3

10.4: Steepest Descent Techniques

Exercise Set 10.4

10.5: Homotopy and Continuation Methods

Exercise Set 10.5

10.6: Numerical Software

Ch 10: Key Concepts

Ch 10: Chapter Review

Ch 11: Boundary-Value Problems for Ordinary Differential Equations

Ch 11: Introduction

11.1: The Linear Shooting Method

Exercise Set 11.1

11.2: The Shooting Method for Nonlinear Problems

Exercise Set 11.2

11.3: Finite-Difference Methods for Linear Problems

Exercise Set 11.3

11.4: Finite-Difference Methods for Nonlinear Problems

Exercise Set 11.4

11.5: The Rayleigh-Ritz Method

Exercise Set 11.5

11.6: Numerical Software

Ch 11: Key Concepts

Ch 11: Chapter Review

Ch 12: Numerical Solutions to Partial Differential Equations

Ch 12: Introduction

12.1: Elliptic Partial Differential Equations

Exercise Set 12.1

12.2: Parabolic Partial Differential Equations

Exercise Set 12.2

12.3: Hyperbolic Partial Differential Equations

Exercise Set 12.3

12.4: An Introduction to the Finite-Element Method

Exercise Set 12.4

12.5: Numerical Software

Ch 12: Key Concepts

Ch 12: Chapter Review

Bibliography

Answers for Selected Exercises

Index

Endsheet-1

Endsheet-2

Endsheet-3

Endsheet-4

For customerâs satisfaction, we provide free samples for any required Textbook solution or test bank to check and evaluate before making the final purchase..