An introduction to numerical analysis for electrical and computer engineers /
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ISBN：9780471467373
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Summary:
Publisher Summary 1
This text is designed for engineers who are not afraid to wade through some fairly abstract math before reaching practical applications. This is not to say, however, that the coverage constitutes a rigorous treatment of the mathematical foundations of numerical analysis. Rather, this is very much a book for engineering students; and although some of the chapters, especially the early ones, have intimidating mathematical titles like functional analysis, orthogonal polynomials, and sequences and series, the examples are generally from engineering, and the most technical proofs are omitted. The author teaches electrical and computer engineering at the University of Alberta, so the examples tend to be drawn from that field; but the underlying techniques are applicable to all fields of engineering, and no background in electrical and computer engineering is required. Annotation 漏2004 Book News, Inc., Portland, OR (booknews.com)
Publisher Summary 2
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 problemsEmphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineeringIncludes MATLAB oriented examplesAn Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
目录
Preface p. xiii
Functional Analysis Ideas p. 1
Introduction p. 1
Some Sets p. 2
Some Special Mappings: Metrics, Norms, and Inner Products p. 4
Metrics and Metric Spaces p. 6
Norms and Normed Spaces p. 8
Inner Products and Inner Product Spaces p. 14
The Discrete Fourier Series (DFS) p. 25
Complex Arithmetic p. 28
Elementary Logic p. 31
References p. 32
Problems p. 33
Number Representations p. 38
Introduction p. 38
Fixed-Point Representations p. 38
Floating-Point Representations p. 42
Rounding Effects in Dot Product Computation p. 48
Machine Epsilon p. 53
Review of Binary Number Codes p. 54
References p. 59
Problems p. 59
Sequences and Series p. 63
Introduction p. 63
Cauchy Sequences and Complete Spaces p. 63
Pointwise Convergence and Uniform Convergence p. 70
Fourier Series p. 73
Taylor Series p. 78
Asymptotic Series p. 97
More on the Dirichlet Kernel p. 103
Final Remarks p. 107
COordinate Rotation DIgital Computing (CORDIC) p. 107
Introduction p. 107
The Concept of a Discrete Basis p. 108
Rotating Vectors in the Plane p. 112
Computing Arctangents p. 114
Final Remarks p. 115
Mathematical Induction p. 116
Catastrophic Cancellation p. 117
References p. 119
Problems p. 120
Linear Systems of Equations p. 127
Introduction p. 127
Least-Squares Approximation and Linear Systems p. 127
Least-Squares Approximation and Ill-Conditioned Linear Systems p. 132
Condition Numbers p. 135
LU Decomposition p. 148
Least-Squares Problems and QR Decomposition p. 161
Iterative Methods for Linear Systems p. 176
Final Remarks p. 186
Hilbert Matrix Inverses p. 186
SVD and Least Squares p. 191
References p. 193
Problems p. 194
Orthogonal Polynomials p. 207
Introduction p. 207
General Properties of Orthogonal Polynomials p. 207
Chebyshev Polynomials p. 218
Hermite Polynomials p. 225
Legendre Polynomials p. 229
An Example of Orthogonal Polynomial Least-Squares Approximation p. 235
Uniform Approximation p. 238
References p. 241
Problems p. 241
Interpolation p. 251
Introduction p. 251
Lagrange Interpolation p. 252
Newton Interpolation p. 257
Hermite Interpolation p. 266
Spline Interpolation p. 269
References p. 284
Problems p. 285
Nonlinear Systems of Equations p. 290
Introduction p. 290
Bisection Method p. 292
Fixed-Point Method p. 296
Newton-Raphson Method p. 305
The Method p. 305
Rate of Convergence Analysis p. 309
Breakdown Phenomena p. 311
Systems of Nonlinear Equations p. 312
Fixed-Point Method p. 312
Newton-Raphson Method p. 318
Chaotic Phenomena and a Cryptography Application p. 323
References p. 332
Problems p. 333
Unconstrained Optimization p. 341
Introduction p. 341
Problem Statement and Preliminaries p. 341
Line Searches p. 345
Newton's Method p. 353
Equality Constraints and Lagrange Multipliers p. 357
MATLAB Code for Golden Section Search p. 362
References p. 364
Problems p. 364
Numerical Integration and Differentiation p. 369
Introduction p. 369
Trapezoidal Rule p. 371
Simpson's Rule p. 378
Gaussian Quadrature p. 385
Romberg Integration p. 393
Numerical Differentiation p. 401
References p. 406
Problems p. 406
Numerical Solution of Ordinary Differential Equations p. 415
Introduction p. 415
First-Order ODEs p. 421
Systems of First-Order ODEs p. 442
Multistep Methods for ODEs p. 455
Adams-Bashforth Methods p. 459
Adams-Moulton Methods p. 461
Comments on the Adams Families p. 462
Variable-Step-Size (Adaptive) Methods for ODEs p. 464
Stiff Systems p. 467
Final Remarks p. 469
MATLAB Code for Example 10.8 p. 469
MATLAB Code for Example 10.13 p. 470
References p. 472
Problems p. 473
Numerical Methods for Eigenproblems p. 480
Introduction p. 480
Review of Eigenvalues and Eigenvectors p. 480
The Matrix Exponential p. 488
The Power Methods p. 498
QR Iterations p. 508
References p. 518
Problems p. 519
Numerical Solution of Partial Differential Equations p. 525
Introduction p. 525
A Brief Overview of Partial Differential Equations p. 525
Applications of Hyperbolic PDEs p. 528
The Vibrating String p. 528
Plane Electromagnetic Waves p. 534
The Finite-Difference (FD) Method p. 545
The Finite-Difference Time-Domain (FDTD) Method p. 550
MATLAB Code for Example 12.5 p. 557
References p. 560
Problems p. 561
An Introduction to MATLAB p. 565
Introduction p. 565
Startup p. 565
Some Basic Operators, Operations, and Functions p. 566
Working with Polynomials p. 571
Loops p. 572
Plotting and M-Files p. 573
References p. 577
Index p. 579
Functional Analysis Ideas p. 1
Introduction p. 1
Some Sets p. 2
Some Special Mappings: Metrics, Norms, and Inner Products p. 4
Metrics and Metric Spaces p. 6
Norms and Normed Spaces p. 8
Inner Products and Inner Product Spaces p. 14
The Discrete Fourier Series (DFS) p. 25
Complex Arithmetic p. 28
Elementary Logic p. 31
References p. 32
Problems p. 33
Number Representations p. 38
Introduction p. 38
Fixed-Point Representations p. 38
Floating-Point Representations p. 42
Rounding Effects in Dot Product Computation p. 48
Machine Epsilon p. 53
Review of Binary Number Codes p. 54
References p. 59
Problems p. 59
Sequences and Series p. 63
Introduction p. 63
Cauchy Sequences and Complete Spaces p. 63
Pointwise Convergence and Uniform Convergence p. 70
Fourier Series p. 73
Taylor Series p. 78
Asymptotic Series p. 97
More on the Dirichlet Kernel p. 103
Final Remarks p. 107
COordinate Rotation DIgital Computing (CORDIC) p. 107
Introduction p. 107
The Concept of a Discrete Basis p. 108
Rotating Vectors in the Plane p. 112
Computing Arctangents p. 114
Final Remarks p. 115
Mathematical Induction p. 116
Catastrophic Cancellation p. 117
References p. 119
Problems p. 120
Linear Systems of Equations p. 127
Introduction p. 127
Least-Squares Approximation and Linear Systems p. 127
Least-Squares Approximation and Ill-Conditioned Linear Systems p. 132
Condition Numbers p. 135
LU Decomposition p. 148
Least-Squares Problems and QR Decomposition p. 161
Iterative Methods for Linear Systems p. 176
Final Remarks p. 186
Hilbert Matrix Inverses p. 186
SVD and Least Squares p. 191
References p. 193
Problems p. 194
Orthogonal Polynomials p. 207
Introduction p. 207
General Properties of Orthogonal Polynomials p. 207
Chebyshev Polynomials p. 218
Hermite Polynomials p. 225
Legendre Polynomials p. 229
An Example of Orthogonal Polynomial Least-Squares Approximation p. 235
Uniform Approximation p. 238
References p. 241
Problems p. 241
Interpolation p. 251
Introduction p. 251
Lagrange Interpolation p. 252
Newton Interpolation p. 257
Hermite Interpolation p. 266
Spline Interpolation p. 269
References p. 284
Problems p. 285
Nonlinear Systems of Equations p. 290
Introduction p. 290
Bisection Method p. 292
Fixed-Point Method p. 296
Newton-Raphson Method p. 305
The Method p. 305
Rate of Convergence Analysis p. 309
Breakdown Phenomena p. 311
Systems of Nonlinear Equations p. 312
Fixed-Point Method p. 312
Newton-Raphson Method p. 318
Chaotic Phenomena and a Cryptography Application p. 323
References p. 332
Problems p. 333
Unconstrained Optimization p. 341
Introduction p. 341
Problem Statement and Preliminaries p. 341
Line Searches p. 345
Newton's Method p. 353
Equality Constraints and Lagrange Multipliers p. 357
MATLAB Code for Golden Section Search p. 362
References p. 364
Problems p. 364
Numerical Integration and Differentiation p. 369
Introduction p. 369
Trapezoidal Rule p. 371
Simpson's Rule p. 378
Gaussian Quadrature p. 385
Romberg Integration p. 393
Numerical Differentiation p. 401
References p. 406
Problems p. 406
Numerical Solution of Ordinary Differential Equations p. 415
Introduction p. 415
First-Order ODEs p. 421
Systems of First-Order ODEs p. 442
Multistep Methods for ODEs p. 455
Adams-Bashforth Methods p. 459
Adams-Moulton Methods p. 461
Comments on the Adams Families p. 462
Variable-Step-Size (Adaptive) Methods for ODEs p. 464
Stiff Systems p. 467
Final Remarks p. 469
MATLAB Code for Example 10.8 p. 469
MATLAB Code for Example 10.13 p. 470
References p. 472
Problems p. 473
Numerical Methods for Eigenproblems p. 480
Introduction p. 480
Review of Eigenvalues and Eigenvectors p. 480
The Matrix Exponential p. 488
The Power Methods p. 498
QR Iterations p. 508
References p. 518
Problems p. 519
Numerical Solution of Partial Differential Equations p. 525
Introduction p. 525
A Brief Overview of Partial Differential Equations p. 525
Applications of Hyperbolic PDEs p. 528
The Vibrating String p. 528
Plane Electromagnetic Waves p. 534
The Finite-Difference (FD) Method p. 545
The Finite-Difference Time-Domain (FDTD) Method p. 550
MATLAB Code for Example 12.5 p. 557
References p. 560
Problems p. 561
An Introduction to MATLAB p. 565
Introduction p. 565
Startup p. 565
Some Basic Operators, Operations, and Functions p. 566
Working with Polynomials p. 571
Loops p. 572
Plotting and M-Files p. 573
References p. 577
Index p. 579
An introduction to numerical analysis for electrical and computer engineers /
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