Mathematical techniques for engineers and scientists

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Title:

Personal Author:

Andrews, Larry C.

Publication Information:

Bellingham, WA : SPIE Press, 2003

ISBN:

9780819445063

Subject Term:

Mathematical analysis

Added Author:

Phillips, Ronald L.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010103612	QA300 A52 2003	Open Access Book	Book	Searching... Unknown

As technology continues to move ahead, modern engineers and scientists are frequently faced with difficult mathematical problems that require an ever greater understanding of advanced concepts. This mathematics book is designed as a self-study text for practicing engineers and scientists, and as a useful reference source to complement more comprehensive publications. It takes the reader frorh ordinary differential equations to more sophisticated mathematics--Fourier analysis, vector and tensor analysis, complex variables, partial differential equations, and random processes. The emphasis is on the use of mathematical tools and techniques. The general exposition and choice of topics appeals to a wide audience of applied practitioners.

Preface	p. xi
Symbols and Notation	p. xv
1 Ordinary Differential Equations	p. 1
1.1 Introduction	p. 2
1.2 Classifications	p. 3
1.3 First-Order Equations	p. 6
1.4 Second-Order Linear Equations	p. 17
1.5 Power Series Method	p. 34
1.6 Solutions Near an Ordinary Point	p. 35
1.7 Legendre's Equation	p. 40
1.8 Solutions Near a Singular Point	p. 43
1.9 Bessel's Equation	p. 50
Suggested Reading	p. 57
Exercises	p. 58
2 Special Functions	p. 61
2.1 Introduction	p. 62
2.2 Engineering Functions	p. 63
2.3 Functions Defined by Integrals	p. 67
2.4 Orthogonal Polynomials	p. 76
2.5 Family of Bessel Functions	p. 83
2.6 Family of Hypergeometric-like Functions	p. 94
2.7 Summary of Notations for Special Functions	p. 103
Suggested Reading	p. 104
Exercises	p. 105
3 Matrix Methods and Linear Vector Spaces	p. 109
3.1 Introduction	p. 110
3.2 Basic Matrix Concepts and Operations	p. 110
3.3 Linear Systems of Equations	p. 114
3.4 Linear Systems of Differential Equations	p. 121
3.5 Linear Vector Spaces	p. 133
Suggested Reading	p. 140
Exercises	p. 140
4 Vector Analysis	p. 143
4.1 Introduction	p. 145
4.2 Cartesian Coordinates	p. 146
4.3 Tensor Notation	p. 156
4.4 Vector Functions of One Variable	p. 161
4.5 Scalar and Vector Fields	p. 170
4.6 Line and Surface Integrals	p. 179
4.7 Integral Relations Between Line, Surface, Volume Integrals	p. 194
4.8 Electromagnetic Theory	p. 206
Suggested Reading	p. 210
Exercises	p. 211
5 Tensor Analysis	p. 215
5.1 Introduction	p. 216
5.2 Tensor Notation	p. 216
5.3 Rectilinear Coordinates	p. 218
5.4 Base Vectors	p. 226
5.5 Vector Algebra	p. 231
5.6 Relations Between Tensor Components	p. 238
5.7 Reduction of Tensors to Principal Axes	p. 241
5.8 Tensor Calculus: Rectilinear Coordinates	p. 243
5.9 Curvilinear Coordinates	p. 245
5.10 Tensor Calculus: Curvilinear Coordinates	p. 250
5.11 Riemann-Christoffel Curvature Tensor	p. 259
5.12 Applications	p. 260
Suggested Reading	p. 266
Exercises	p. 266
6 Complex Variables	p. 271
6.1 Introduction	p. 273
6.2 Basic Concepts: Complex Numbers	p. 273
6.3 Complex Functions	p. 281
6.4 The Complex Derivative	p. 287
6.5 Elementary Functions--Part I	p. 295
6.6 Elementary Functions--Part II	p. 300
6.7 Mappings by Elementary Functions	p. 306
Exercises	p. 316
7 Complex Integration, Laurent Series, and Residues	p. 319
7.1 Introduction	p. 320
7.2 Line Integrals in the Complex Plane	p. 320
7.3 Cauchy's Theory of Integration	p. 325
7.4 Infinite Series	p. 339
7.5 Residue Theory	p. 357
7.6 Evaluation of Real Integrals	p. 363
7.7 Evaluation of Real Integrals--Part II	p. 371
7.8 Harmonic Functions Revisited	p. 376
7.9 Heat Conduction	p. 383
7.10 Two-Dimensional Fluid Flow	p. 386
7.11 Flow Around Obstacles	p. 393
Suggested Reading	p. 399
Exercises	p. 400
8 Fourier Series, Eigenvalue Problems, and Green's Function	p. 403
8.1 Introduction	p. 405
8.2 Fourier Trigonometric Series	p. 405
8.3 Power Signals: Exponential Fourier Series	p. 416
8.4 Eigenvalue Problems and Orthogonal Functions	p. 420
8.5 Green's Function	p. 438
Suggested Reading	p. 449
Exercises	p. 450
9 Fourier and Related Transforms	p. 453
9.1 Introduction	p. 454
9.2 Fourier Integral Representation	p. 454
9.3 Fourier Transforms in Mathematics	p. 458
9.4 Fourier Transforms in Engineering	p. 461
9.5 Properties of the Fourier Transform	p. 466
9.6 Linear Shift-Invariant Systems	p. 471
9.7 Hilbert Transforms	p. 473
9.8 Two-Dimensional Fourier Transforms	p. 477
9.9 Fractional Fourier Transform	p. 483
9.10 Wavelets	p. 487
Suggested Reading	p. 492
Exercises	p. 493
10 Laplace, Hankel, and Mellin Transforms	p. 495
10.1 Introduction	p. 496
10.2 Laplace Transform	p. 496
10.3 Initial Value Problems	p. 508
10.4 Hankel Transform	p. 513
10.5 Mellin Transform	p. 519
10.6 Applications Involving the Mellin Transform	p. 526
10.7 Discrete Fourier Transform	p. 529
10.8 Z-Transform	p. 533
10.9 Walsh Transform	p. 538
Suggested Reading	p. 542
Exercises	p. 542
11 Calculus of Variations	p. 545
11.1 Introduction	p. 546
11.2 Functionals and Extremals	p. 547
11.3 Some Classical Variational Problems	p. 552
11.4 Variational Notation	p. 555
11.5 Other Types of Functionals	p. 559
11.6 Isoperimetric Problems	p. 564
11.7 Rayleigh-Ritz Approximation Method	p. 567
11.8 Hamilton's Principle	p. 572
11.9 Static Equilibrium of Deformable Bodies	p. 579
11.10 Two-Dimensional Variational Problems	p. 581
Suggested Reading	p. 584
Exercises	p. 584
12 Partial Differential Equations	p. 589
12.1 Introduction	p. 591
12.2 Classification of Second-Order PDEs	p. 591
12.3 The Heat Equation	p. 592
12.4 The Wave Equation	p. 600
12.5 The Equation of Laplace	p. 604
12.6 Generalized Fourier Series	p. 611
12.7 Applications Involving Bessel Functions	p. 617
12.8 Transform Methods	p. 621
Suggested Reading	p. 631
Exercises	p. 632
13 Probability and Random Variables	p. 637
13.1 Introduction	p. 638
13.2 Random Variables and Probability Distributions	p. 640
13.3 Examples of Density Functions	p. 646
13.4 Expected Values	p. 649
13.5 Conditional Probability	p. 655
13.6 Functions of One Random Variable	p. 658
13.7 Two Random Variables	p. 665
13.8 Functions of Two or More Random Variables	p. 677
13.9 Limit Distributions	p. 690
Suggested Reading	p. 692
Exercises	p. 693
14 Random Processes	p. 697
14.1 Introduction	p. 698
14.2 Probabilistic Description of Random Process	p. 698
14.3 Autocorrelation and Autocovariance Functions	p. 700
14.4 Cross-Correlation and Cross-Covariance	p. 708
14.5 Power Spectral Density Functions	p. 711
14.6 Transformations of Random Processes	p. 716
14.7 Stationary Gaussian Processes	p. 722
Suggested Reading	p. 729
Exercises	p. 729
15 Applications	p. 733
15.1 Introduction	p. 734
15.2 Mechanical Vibrations and Electric Circuits	p. 734
15.3 Buckling of a Long Column	p. 742
15.4 Communication Systems	p. 745
15.5 Applications in Geometrical Optics	p. 756
15.6 Wave Propagation in Free Space	p. 762
15.7 ABCD Matrices for Paraxial Systems	p. 767
15.8 Zernike Polynomials	p. 773
Exercises	p. 780
References	p. 783
Index	p. 785

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