Christopher J. Zarowski
An Introduction to Numerical Analysis for Electrical and Computer Engineers
Christopher J. Zarowski
An Introduction to Numerical Analysis for Electrical and Computer Engineers
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_ This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems _ Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering _ Includes MATLAB oriented examples
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_ This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems
_ Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering
_ Includes MATLAB oriented examples
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
_ Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering
_ Includes MATLAB oriented examples
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 604
- Erscheinungstermin: 13. April 2004
- Englisch
- Abmessung: 240mm x 161mm x 37mm
- Gewicht: 965g
- ISBN-13: 9780471467373
- ISBN-10: 0471467375
- Artikelnr.: 12664263
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 604
- Erscheinungstermin: 13. April 2004
- Englisch
- Abmessung: 240mm x 161mm x 37mm
- Gewicht: 965g
- ISBN-13: 9780471467373
- ISBN-10: 0471467375
- Artikelnr.: 12664263
CHRISTOPHER J. ZAROWSKI, PhD, is an associate professor in the Department of Electrical and Computer Engineering at the University of Alberta, Canada. He has authored more than fifty journal articles and conference papers and is a senior member of the IEEE.
Preface. 1 Functional Analysis Ideas. 1.1 Introduction. 1.2 Some Sets. 1.3
Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete
Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B
Elementary Logic. References. Problems. 2 Number Representations. 2.1
Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point
Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5
Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References.
Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences
and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4
Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the
Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation
DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a
Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing
Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction.
Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear
Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and
Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear
Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares
Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems.
4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD
and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1
Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3
Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials.
5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7
Uniform Approximation. References. Problems. 6 Interpolation. 6.1
Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4
Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7
Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3
Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear
Equations. 7.6 Chaotic Phenomena and a Cryptography Application.
References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2
Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's
Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A
MATLAB Code for Golden Section Search. References. Problems. 9 Numerical
Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule.
9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6
Numerical Differentiation. References. Problems. 10 Numerical Solution of
Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs.
10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5
Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7
Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B
MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods
for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and
Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR
Iterations. References. Problems. 12 Numerical Solution of Partial
Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial
Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The
Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain
(FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References.
Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup.
13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with
Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.
Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete
Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B
Elementary Logic. References. Problems. 2 Number Representations. 2.1
Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point
Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5
Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References.
Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences
and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4
Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the
Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation
DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a
Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing
Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction.
Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear
Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and
Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear
Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares
Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems.
4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD
and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1
Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3
Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials.
5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7
Uniform Approximation. References. Problems. 6 Interpolation. 6.1
Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4
Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7
Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3
Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear
Equations. 7.6 Chaotic Phenomena and a Cryptography Application.
References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2
Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's
Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A
MATLAB Code for Golden Section Search. References. Problems. 9 Numerical
Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule.
9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6
Numerical Differentiation. References. Problems. 10 Numerical Solution of
Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs.
10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5
Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7
Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B
MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods
for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and
Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR
Iterations. References. Problems. 12 Numerical Solution of Partial
Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial
Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The
Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain
(FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References.
Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup.
13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with
Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.
Preface. 1 Functional Analysis Ideas. 1.1 Introduction. 1.2 Some Sets. 1.3
Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete
Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B
Elementary Logic. References. Problems. 2 Number Representations. 2.1
Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point
Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5
Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References.
Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences
and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4
Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the
Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation
DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a
Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing
Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction.
Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear
Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and
Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear
Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares
Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems.
4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD
and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1
Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3
Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials.
5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7
Uniform Approximation. References. Problems. 6 Interpolation. 6.1
Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4
Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7
Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3
Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear
Equations. 7.6 Chaotic Phenomena and a Cryptography Application.
References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2
Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's
Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A
MATLAB Code for Golden Section Search. References. Problems. 9 Numerical
Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule.
9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6
Numerical Differentiation. References. Problems. 10 Numerical Solution of
Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs.
10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5
Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7
Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B
MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods
for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and
Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR
Iterations. References. Problems. 12 Numerical Solution of Partial
Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial
Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The
Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain
(FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References.
Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup.
13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with
Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.
Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete
Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B
Elementary Logic. References. Problems. 2 Number Representations. 2.1
Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point
Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5
Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References.
Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences
and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4
Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the
Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation
DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a
Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing
Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction.
Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear
Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and
Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear
Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares
Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems.
4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD
and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1
Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3
Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials.
5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7
Uniform Approximation. References. Problems. 6 Interpolation. 6.1
Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4
Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7
Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3
Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear
Equations. 7.6 Chaotic Phenomena and a Cryptography Application.
References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2
Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's
Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A
MATLAB Code for Golden Section Search. References. Problems. 9 Numerical
Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule.
9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6
Numerical Differentiation. References. Problems. 10 Numerical Solution of
Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs.
10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5
Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7
Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B
MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods
for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and
Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR
Iterations. References. Problems. 12 Numerical Solution of Partial
Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial
Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The
Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain
(FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References.
Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup.
13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with
Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.