Başlık:
Applied numerical analysis
Yazar:
Gerald, Curtis F., 1915-
ISBN:
9780201870725
Ek Yazar:
Edition:
6th ed.
Yayım Bilgisi:
Reading, Mass. : Addison-Wesley, c1999.
Fiziksel Tanım:
1 v. (various pagings) : ill. ; 25 cm.
Konu Terimleri:
Added Author:
Mevcut:*
Library | Materyal Türü | Barkod | Yer Numarası | Durum |
|---|---|---|---|---|
Searching... Pamukkale Merkez Kütüphanesi | Kitap | 0017465 | QA297.G47 1999 | Searching... Unknown |
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Özet
Özet
Application-based aproach, incorporating technology; great for applied sciences and engineering students. *Organization of final chapters which includes gathering the material on finite elements from several chapters into one chapter. *Computer programs in either Fortran 90 or C are given at the conclusion of each chapter. The computer algebra system MATLAB has been added (with several comparisons to Maple and Mathematica) as well as addressing the use of the advanced calculator. *The chapter on approximations of functions has been moved forward in the text. *More problems which are challenging have been added to the end of the exercise sets.
Table of Contents
| Numerical Computing and Computers |
| Introduction |
| Using a Computer to Do Numerical Analysis |
| A Typical Example |
| Implementing Bisection |
| Computer Arithmetic and Errors |
| Theoretical Matters |
| Parallel and Distributed Computing |
| Chapter Summary |
| Exercises |
| Solving Nonlinear Equations |
| Pressure Drop for a Flowing Fluid |
| Interval Halving (Bisection) Revisited |
| Linear Interpolation Methods |
| Newton''s Method |
| Muller''s Method |
| Fixed-Point Iteration: x = g(x) Method |
| Newton''s Method for Polynomials |
| Bairstow''s Method for Quadratic Factors |
| Other Methods for Polynomials |
| Multiple Roots |
| Theoretical Matters |
| Using MATLAB |
| Chapter Summary |
| Computer Programs |
| Exercises |
| Solving Sets of Equations |
| Applications of Sets of Equations |
| Matrix Notation |
| The Elimination Method |
| Gaussian Elimination and Gauss-Jordan Methods |
| Other Direct Methods |
| Pathology in Linear SystemsSingular Matrices |
| Determinants and Matrix Inversion |
| Norms |
| Condition Numbers and Errors in Solutions |
| Iterative Methods |
| Relaxation Method |
| Systems of Nonlinear Equations |
| Theoretical Matters |
| Using Maple and MATLAB |
| Parallel Processing |
| Chapter Summary |
| Computer Programs |
| Exercises |
| Interpolation and Curve Fitting |
| An Interpolation Problem |
| Lagrangian Polynomials |
| Divided Differences |
| Interpolating with a Cubic Spline |
| Bezier Curves and B-Spline Curves |
| Polynomial Approximation of Surfaces |
| Least-Squares Approximations |
| Theoretical Matters |
| Using MATLAB and Mathematica |
| Chapter Summary |
| Computer Programs |
| Exercises |
| Approximation of Functions |
| Chebyshev Polynomials |
| Economized Power Series |
| Approximation with Rational Functions |
| Fourier Series |
| Theoretical Matters |
| Using Computer Algebra Systems |
| Chapter Summary |
| Computer Program |
| Exercises |
| Numerical Differentiation and Numerical Integration |
| Getting Derivatives and Integrals Numerically |
| Derivatives from Difference Tables |
| Higher-Order Derivatives |
| Extrapolation Techniques |
| Newton-Cotes Integration Formulas |
| The Trapezoidal RuleA Composite Formula |
| Simpson''s Rules |
| Other Ways to Derive Integration Formulas |
| Gaussian Quadrature |
| Adaptive Integration |
| Multiple Integrals |
| Multiple Integration with Variable Limits |
| Applications of Cubic Splines |
| An Application of Numerical IntegrationFourier Transforms |
| Theoretical Matters |
| Using MATLAB |
| Parallel Processing |
| Chapter Summary |
| Computer Programs |
| Exercises |
| Numerical Solution of Ordinary Differential Equations |
| The Spring-Mass ProblemA Variation |
| Taylor-Series Method |
| Euler and Modified Euler Methods |
| Runge-Kutta Methods |
| Multistep Methods |
| Milne''s Method |
| Adams-Moulton Method |
| Convergence Criteria |
| Systems of Equations and Higher-Order Equations |
| Comparison of Methods Stiff Equations |
| Theoretical Matters |
| Using Maple and MATLAB |
| Chapter Summary |
| Computer Programs |
| Exercises |
| Boundary-Value Problems |
| Temperature Distribution in a Rod |
| The Shooting Method |
| Solution Through a Set of Equations |
| Derivative Boundary Conditions |
| Characteristic-Value Problems |
| Temperature Distribution in a Slab |
| Solving for the Temperatures in a Slab |
| The Alternating Direction Implicit Method |
| Irregular Regions and Nonrectangular Grids |
| Theoretical Matters |
| Using MATLAB |
| Chapter Summary |
| Computer Programming |
| Parallel Processing |
| Exercises |
| Parabolic and Hyperbolic Partial-Differential Equations |
| Types of Partial-Differential Equations |
| The Heat Equation and the Wave Equation |
| Solution Techniques for the Heat Equation in One Dimension |
| Solving the Vibrating String Problem |
| Parabolic Equations in Two or Three Dimensions |
| The Wave Equation in Two Dimensions |
| Theoretical Matters |
| Chapter Summary |
| Computer Programs |
| Exercises |
| The Finite Element Method |
| The Rayleigh-Ritz Method |
| Collocation and Galerkin Methods |
| Finite Elements for an Ordinary-Differential Equation |
| Finite Elements for an Elliptic Partial-Differential Equation |
| Finite Elements for Parabolic and Hyperbolic Equations |
| Theoretical Matters |
| Chapter Summary |
| Computer Program |
| Exercises |
| Appendices |
| Some Basic Information from Calculus |
| Deriving Formulas by the Method of Undetermined Coefficients |
| Software Resources |
| Answers to Selected Exercises |
| References |
| Index |
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