Numerical Methods for Engineering and Scientists

ISBN-10: 0824704436

ISBN-13: 9780824704438

Edition: 2nd 2001 (Revised)

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Book details

List price: $132.95
Edition: 2nd
Copyright year: 2001
Publisher: CRC Press LLC
Publication date: 5/31/2001
Binding: Hardcover
Pages: 840
Size: 7.40" wide x 10.00" long x 2.30" tall
Weight: 4.554
Language: English

Preface
Introduction
Objectives and Approach
Organization of the Book
Examples
Programs
Problems
Significant Digits, Precision, Accuracy, Errors, and Number Representation
Software Packages and Libraries
The Taylor Series and the Taylor Polynomial
Basic Tools of Numerical Analysis
Systems of Linear Algebraic Equations
Eigenproblems
Roots of Nonlinear Equations
Polynomial Approximation and Interpolation
Numercial Differentiation and Difference Formulas
Numerical Integration
Summary
Systems of Linear Algebraic Equations
Introduction
Properties of Matrices and Determinants
Direct Elimination Methods
LU Factorization
Tridiagonal Systems of Equations
Pitfalls of Elimination Methods
Iterative Methods
Programs
Summary
Exercise Problems
Eigenproblems
Introduction
Mathematical Characteristics of Eigenproblems
The Power Method
The Direct Method
The QR Method
Eigenvectors
Other Methods
Programs
Summary
Exercise Problems
Nonlinear Equations
Introduction
General Features of Root Finding
Closed Domain (Bracketing) Methods
Open Domain Methods
Polynomials
Pitfalls of Root Finding Methods and Other Methods of Root Finding
Systems of Nonlinear Equations
Programs
Summary
Exercise Problems
Polynomial Approximation and Interpolation
Introduction
Properties of Polynomials
Direct Fit Polynomials
Lagrange Polynomials
Divided Difference Tables and Divided Difference Polynomials
Difference Tables and Difference Polynomials
Inverse Interpolation
Multivariate Approximation
Cubic Splines
Least Squares Approximation
Programs
Summary
Exercise Problems
Numerical Differentiation and Difference Formulas
Introduction
Unequally Spaced Data
Equally Spaced Data
Taylor Series Approach
Difference Formulas
Error Estimation and Extrapolation
Programs
Summary
Exercise Problems
Numerical Integration
Introduction
Direct Fit Polynomials
Newton-Cotes Formulas
Extrapolation and Romberg Integration
Adaptive Integration
Gaussian Quadrature
Multiple Integrals
Programs
Summary
Exercise Problems
Ordinary Differential Equations
Introduction
General Features of Ordinary Differential Equations
Classification of Ordinary Differential Equations
Classification of Physical Problems
Initial-Value Ordinary Differential Equations
Boundary-Value Ordinary Differential Equations
Summary
One-Dimensional Initial-Value Ordinary Differential Equations
Introduction
General Features of Initial-Value ODEs
The Taylor Series Method
The Finite Difference Method
The First-Order Euler Methods
Consistency, Order, Stability, and Convergence
Single-Point Methods
Extrapolation Methods
Multipoint Methods
Summary of Methods and Results
Nonlinear Implicit Finite Difference Equations
Higher-Order Ordinary Differential Equations
Systems of First-Order Ordinary Differential Equations
Stiff Ordinary Differential Equations
Programs
Summary
Exercise Problems
One-Dimensional Boundary-Value Ordinary Differential Equations
Introduction
General Features of Boundary-Value ODEs
The Shooting (Initial-Value) Method
The Equilibrium (Boundary-Value) Method
Derivative (and Other) Boundary Conditions
Higher-Order Equilibrium Methods
The Equilibrium Method for Nonlinear Boundary-Value Problems
The Equilibrium Method on Nonuniform Grids
Eigenproblems
Programs
Summary
Exercise Problems
Partial Differential Equations
Introduction
General Features of Partial Differential Equations
Classification of Partial Differential Equations
Classification of Physical Problems
Elliptic Partial Differential Equations
Parabolic Partial Differential Equations
Hyperbolic Partial Differential Equations
The Convection-Diffusion Equation
Initial Values and Boundary Conditions
Well-Posed Problems
Summary
Elliptic Partial Differential Equations
Introduction
General Features of Elliptic PDEs
The Finite Difference Method
Finite Difference Solution of the Laplace Equation
Consistency, Order, and Convergence
Iterative Methods of Solution
Derivative Boundary Conditions
Finite Difference Solution of the Poisson Equation
Higher-Order Methods
Nonrectangular Domains
Nonlinear Equations and Three-Dimensional Problems
The Control Volume Method
Programs
Summary
Exercise Problems
Parabolic Partial Differential Equations
Introduction
General Features of Parabolic PDEs
The Finite Difference Method
The Forward-Time Centered-Space (FTCS) Method
Consistency, Order, Stability, and Convergence
The Richardson and DuFort-Frankel Methods
Implicit Methods
Derivative Boundary Conditions
Nonlinear Equations and Multidimensional Problems
The Convection-Diffusion Equation
Asymptotic Steady State Solution to Propagation Problems
Programs
Summary
Exercise Problems
Hyperbolic Partial Differential Equations
Introduction
General Features of Hyperbolic PDEs
The Finite Difference Method
The Forward-Time Centered-Space (FTCS) Method and the Lax Method
Lax-Wendroff Type Methods
Upwind Methods
The Backward-Time Centered-Space (BTCS) Method
Nonlinear Equations and Multidimensional Problems
The Wave Equation
Programs
Summary
Exercise Problems
The Finite Element Method
Introduction
The Rayleigh-Ritz, Collocation, and Galerkin Methods
The Finite Element Method for Boundary Value Problems
The Finite Element Method for the Laplace (Poisson) Equation
The Finite Element Method for the Diffusion Equation
Programs
Summary
Exercise Problems
References
Answers to Selected Problems
Index
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