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More copies of this ISBNThis title in other editionsOther titles in the Featured Titles for Numerical Analysis series:Applied Numerical Analysisby Curtis F. Gerald
Synopses & ReviewsPublisher Comments:The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theorybased sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.
Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis
For all readers interested in applied numerical analysis. Synopsis:The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theorybased sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.
Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis
For all readers interested in applied numerical analysis. Table of Contents0. Preliminaries.
Analysis versus Numerical Analysis.
Computers and Numerical Analysis.
An Illustrative Example.
Kinds of Errors in Numerical Procedures.
Interval Arithmetic.
Parallel and Distributed Computing.
Measuring the Efficiency of Procedures.
1. Solving Nonlinear Equations.
Interval Halving (Bisection).
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
FixedPoint Iteration.
Other Methods.
Nonlinear Systems.
2. Solving Sets of Equations.
Matrices and Vectors.
Elimination Methods.
The Inverse of a Matrix and Matrix Pathology.
Almost Singular Matrices  Condition Numbers.
Interactive Methods.
Parallel Processing.
3. Interpolation and Curve Fitting.
Interpolating Polynomials.
Divided Differences.
Spline Curves.
Bezier Curves and BSplines.
Interpolating on a Surface.
Least Squares Approximations.
4. Approximation of Functions.
Chebyshev Polynomials and Chebyshev Series.
Rational Function Approximations.
Fourier Series.
5. Numerical Differentiation and Integration.
Differentiation with a Computer.
Numerical Integration  The Trapezoidal Rule.
Simpson's Rules.
An Application of Numerical Integration  Fourier Series and Fourier Transforms Adaptive Integration.
Gaussian Quadrature.
Multiple Integrals.
Applications of Cubic Splines.
6. Numerical Solution of Ordinary Differential Equations.
The Taylor Series Method.
The Euler Method and Its Modification.
RungeKutta Methods.
Multistep Methods.
HigherOrder Equations and Systems.
Stiff Equations.
BoundaryValue Problems.
CharacteristicValue Problems.
7. Optimization.
Finding the Minimum of y = f(x).
Minimizing a Function of Several Variables.
Linear Programming.
Nonlinear Programming.
Other Optimizations.
8. Partial Differential Equations.
Elliptic Equations.
Parabolic Equations.
Hyperbolic Equations.
9. Finite Element Analysis.
Mathematical Background.
Finite Elements for Ordinary Differential Equation.
Finite Elements for Partial Differential Equation.
Appendices.
A. Some Basic Information from Calculus.
B. Software Resources.
Answers to Selected Exercises.
References.
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