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Test bank for Numerical Analysis 10th Edition by Richard L. Burden

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Test bank for Numerical Analysis 10th Edition by Richard L. Burden
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Test bank for Numerical Analysis 10th Edition by Richard L. Burden

Test bank for Numerical Analysis 10th Edition by Richard L. Burden

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: Newton’s 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 Müller’s 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 Neville’s 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: Richardson’s 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: Euler’s 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: Householder’s 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: Newton’s 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
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Test bank for Numerical Analysis 10th Edition by Richard L. Burden