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Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.
Table of Contents
|Review of Taylor Series|
|Floating-Point Representation And Errors|
|Loss of Significance|
|Locating Roots Of Equations|
|Interpolation And Numerical Differentiation|
|Errors in Polynomial Interpolation|
|Estimating Derivatives and Richardson Extrapolation|
|Lower and Upper Sums|
|Additional Topics On Numerical Integration|
|Simpson+s Rule and Adaptive Simpson+s Rule|
|Gaussian Quadrature Formulas|
|Systems Of Linear Equations|
|Naive Gaussian Elimination|
|Gaussian Elimination with Scaled Partial Pivoting|
|Tridiagonal and Banded Systems|
|Additional Topics Concerning Systems Of Linear Equations|
|Iterative Solutions of Linear Systems|
|Eigenvalues and Eigenvectors|
|Approximation By Spline Functions|
|First-Degree and Second-Degree Splines|
|Natural Cubic Splines|
|B Splines: Interpolation and Approximation|
|Ordinary Differential Equations|
|Taylor Series Methods|
|Stability and Adaptive Runge-Kutta and Multistep Methods|
|Systems Of Ordinary Differential Equations|
|Methods for First-Order Systems|
|Higher-Order Equations and Systems|
|Smoothing Of Data And The Method Of Least Squares|
|Method of Least Squares|
|Orthogonal Systems and Chebyshev Polynomials|
|Other Examples of the Least-Squares Principle|
|Monte Carlo Methods And Simulation|
|Estimation of Areas and Volumes by Monte Carlo Techniques|
|Boundary-Value Problems For Ordinary Differential Equations|
|Shooting Method Shooting Method Algorithm|
|A Discretization Method|
|Partial Differential Equations|
|Minimization Of Functions|
|Standard Forms and Duality|
|Approximate Solution of Inconsistent Linear Systems|
|Advice On Good Programming Practices|
|Representation Of Numbers In Different Bases|
|Representation of Numbers in Different Bases|
|Additional Details On Ieee Floating-Point Arithmetic|
|More on IEEE Standard Floating-Point Arithmetic|
|Linear Algebra Concepts And Notation|
|Abstract Vector Spaces|
|Answers For Selected Problems|
|Table of Contents provided by Publisher. All Rights Reserved.|