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Summary
Numerous new or revised problems are drawn from actual engineering practice. The expanded breadth of engineering disciplines covered is especially evident in these exercises, which now cover such areas as biotechnology and biomedical engineering. Excellent new examples and case studies span all areas of engineering giving students a broad exposure to various fields in engineering.
Users will find use of files for many popular software packages, specifically MATLAB®, Excel® with VBA, and Mathcad®. There is also material on developing MATLAB® m-files and VBA macros.
Table of Contents
Part 1 Modeling, Computers, and Error Analysis1 Mathematical Modeling and Engineering Problem Solving2 Programming and Software3 Approximations and Round-Off Errors4 Truncation Errors and the Taylor SeriesPart 2 Roots of Equations5 Bracketing Methods 6 Open Methods7 Roots of Polynomials8 Case Studies: Roots of EquationsPart 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
2 Programming and Software3 Approximations and Round-Off Errors4 Truncation Errors and the Taylor SeriesPart 2 Roots of Equations5 Bracketing Methods 6 Open Methods7 Roots of Polynomials8 Case Studies: Roots of EquationsPart 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
4 Truncation Errors and the Taylor SeriesPart 2 Roots of Equations5 Bracketing Methods 6 Open Methods7 Roots of Polynomials8 Case Studies: Roots of EquationsPart 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
5 Bracketing Methods 6 Open Methods7 Roots of Polynomials8 Case Studies: Roots of EquationsPart 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
7 Roots of Polynomials8 Case Studies: Roots of EquationsPart 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
Part 3 Linear Algebraic Equations9 Gauss Elimination10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
10 LU Decomposition and Matrix Inversion11 Special Matrices and Gauss-Seidel12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
12 Case Studies: Linear Algebraic EquationsPart 4 Optimization13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
13 One-Dimensional Unconstrained Optimization14 Multidimensional Unconstrained Optimization15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
15 Constrained Optimization16 Case Studies: OptimizationPart 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
Part 5 Curve Fitting17 Least-Squares Regression18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
18 Interpolation19 Fourier Approximation20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
20 Case Studies: Curve FittingPart 6 Numerical Differentiation and Integration21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
21 Newton-Cotes Integration Formulas22 Integration of Equations23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
23 Numerical Differentiation24 Case Studies: Numerical Integration and DifferentiationPart 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
Part 7 Ordinary Differential Equations25 Runge-Kutta Methods26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
26 Stiffness and Multistep Methods27 Boundary-Value and Eigenvalue Problems28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
28 Case Studies: Ordinary Differential EquationsPart 8 Partial Differential Equations29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
29 Finite Difference: Elliptic Equations30 Finite Difference: Parabolic Equations31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
31 Finite-Element Method32 Case Studies: Partial Differential EquationsAppendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
Appendix A The Fourier SeriesAppendix B Getting Started with MatlabAppendix C Getting Starte dwith MathcadBibliographyIndex
Appendix C Getting Starte dwith MathcadBibliographyIndex
Index
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