Mathematical techniques for engineers and scientists:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Bellingham, Wash.
SPIE Press
2003
|
| Schriftenreihe: | SPIE press monograph
118 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890517&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Abstract: | 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. Designed as a self-study text for practicing engineers and scientists, as well as a useful reference, the book takes the reader from 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. |
| Beschreibung: | Includes bibliographical references (p. 783-784) and index |
| Umfang: | XV, 797 S. ILl., graph. Darst. |
| ISBN: | 0819445061 |
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Datensatz im Suchindex
| _version_ | 1819354056812920832 |
|---|---|
| adam_text | MATHEMATICAL TECHNIQUES FOR ENGINEERS AND SCIENTISTS LARRY C. ANDREWS
RONALD L PHILLIPS SPIE PRESS A PUBLICATION OF SPIE*THE INTERNATIONAL
SOCIETY FOR OPTICAL ENGINEERING BELLINGHAM, WASHINGTON USA CONTENTS
PREFACE /XI SYMBOLS AND NOTATION I XV 1 ORDINARY DIFFERENTIAL EQUATIONS
/ 1 1.1 INTRODUCTION /2 1.2 CLASSIFICATIONS / 3 1.3 FIRST-ORDER
EQUATIONS / 6 1.4 SECOND-ORDER LINEAR EQUATIONS /17 1.5 POWER SERIES
METHOD / 34 1.6 SOLUTIONS NEAR AN ORDINARY POINT / 35 1.7 LEGENDRE S
EQUATION / 40 1.8 SOLUTIONS NEAR A SINGULAR POINT / 43 1.9 BESSEL S
EQUATION / 50 SUGGESTED READING / 57 EXERCISES / 58 2 SPECIAL FUNCTIONS
/ 61 2.1 INTRODUCTION /62 2.2 ENGINEERING FUNCTIONS / 63 2.3 FUNCTIONS
DEFINED BY INTEGRALS / 67 2.4 ORTHOGONAL POLYNOMIALS / 76 2.5 FAMILY OF
BESSEL FUNCTIONS / 83 2.6 FAMILY OF HYPERGEOMETRIC-LIKE FUNCTIONS / 94
2.7 SUMMARY OF NOTATIONS FOR SPECIAL FUNCTIONS /103 SUGGESTED READING
/104 EXERCISES /105 3 MATRIX METHODS AND LINEAR VECTOR SPACES / 10 9 3.1
INTRODUCTION /110 3.2 BASIC MATRIX CONCEPTS AND OPERATIONS /110 3.3
LINEAR SYSTEMS OF EQUATIONS /114 3.4 LINEAR SYSTEMS OF DIFFERENTIAL
EQUATIONS / 121 3.5 LINEAR VECTOR SPACES /133 SUGGESTED READING /140
EXERCISES /140 VI CONTENTS 4 VECTOR ANALYSIS /143 4.1 INTRODUCTION /145
4.2 CARTESIAN COORDINATES /146 4.3 TENSOR NOTATION /156 4.4 VECTOR
FUNCTIONS OF ONE VARIABLE /161 4.5 SCALAR AND VECTOR FIELDS /170 4.6
LINE AND SURFACE INTEGRALS /179 4.7 INTEGRAL RELATIONS BETWEEN LINE,
SURFACE, VOLUME INTEGRALS /194 4.8 ELECTROMAGNETIC THEORY / 206
SUGGESTED READING /210 EXERCISES / 211 5 TENSOR ANALYSIS / 215 5.1
INTRODUCTION /216 5.2 TENSOR NOTATION /216 5.3 RECTILINEAR COORDINATES
/218 5.4 BASE VECTORS /226 5.5 VECTOR ALGEBRA / 231 5.6 RELATIONS
BETWEEN TENSOR COMPONENTS / 238 5.7 REDUCTION OF TENSORS TO PRINCIPAL
AXES / 241 5.8 TENSOR CALCULUS: RECTILINEAR COORDINATES / 243 5.9
CURVILINEAR COORDINATES / 245 5.10 TENSOR CALCULUS: CURVILINEAR
COORDINATES /250 5.11 RIEMANN-CHRISTOFFEL CURVATURE TENSOR / 259 5.12
APPLICATIONS /260 SUGGESTED READING / 266 EXERCISES /266 6 COMPLEX
VARIABLES / 27 1 6.1 INTRODUCTION /273 6.2 BASIC CONCEPTS: COMPLEX
NUMBERS / 273 6.3 COMPLEX FUNCTIONS / 281 6.4 THE COMPLEX DERIVATIVE /
287 6.5 ELEMENTARY FUNCTIONS*PART I / 295 6.6 ELEMENTARY FUNCTIONS*PART
II / 300 6.7 MAPPINGS BY ELEMENTARY FUNCTIONS / 306 EXERCISES /316 7
COMPLEX INTEGRATION, LAURENT SERIES, AND RESIDUES /319 7.1 INTRODUCTION
/320 7.2 LINE INTEGRALS IN THE COMPLEX PLANE / 320 CONTENTS VII 7.3
CAUCHY S THEORY OF INTEGRATION / 325 7.4 INFINITE SERIES / 339 7.5
RESIDUE THEORY /357 7.6 EVALUATION OF REAL INTEGRALS*PART I / 363 7.7
EVALUATION OF REAL INTEGRALS*PART II / 371 7.8 HARMONIC FUNCTIONS
REVISITED / 376 7.9 HEAT CONDUCTION /383 7.10 TWO-DIMENSIONAL FLUID FLOW
/ 386 7.11 FLOW AROUND OBSTACLES / 393 SUGGESTED READING / 399 EXERCISES
/400 8 FOURIER SERIES, EIGENVALUE PROBLEMS, AND GREEN S FUNCTION / 403
8.1 INTRODUCTION /405 8.2 FOURIER TRIGONOMETRIC SERIES / 405 8.3 POWER
SIGNALS: EXPONENTIAL FOURIER SERIES /416 8.4 EIGENVALUE PROBLEMS AND
ORTHOGONAL FUNCTIONS / 420 8.5 GREEN S FUNCTION / 438 SUGGESTED READING
/ 449 EXERCISES / 450 9 FOURIER AND RELATED TRANSFORMS / 453 9.1
INTRODUCTION / 454 9.2 FOURIER INTEGRAL REPRESENTATION / 454 9.3 FOURIER
TRANSFORMS IN MATHEMATICS / 458 9.4 FOURIER TRANSFORMS IN ENGINEERING
/461 9.5 PROPERTIES OF THE FOURIER TRANSFORM / 466 9.6 LINEAR
SHIFT-INVARIANT SYSTEMS / 471 9.7 HILBERT TRANSFORMS /473 9.8
TWO-DIMENSIONAL FOURIER TRANSFORMS / 477 9.9 FRACTIONAL FOURIER
TRANSFORM / 483 9.10 WAVELETS /487 SUGGESTED READING / 492 EXERCISES
/493 10 LAPLACE, HANKEL, AND MELLIN TRANSFORMS / 495 10.1 INTRODUCTION
/496 10.2 LAPLACE TRANSFORM / 496 10.3 INITIAL VALUE PROBLEMS / 508 10.4
HANKEL TRANSFORM / 513 10.5 MELLIN TRANSFORM /519 10.6 APPLICATIONS
INVOLVING THE MELLIN TRANSFORM / 526 10.7 DISCRETE FOURIER TRANSFORM
/529 VIII CONTENTS 10.8 Z-TRANSFORM /533 10.9 WALSH TRANSFORM / 538
SUGGESTED READING / 542 EXERCISES /542 11 CALCULUS OF VARIATIONS / 545
11.1 INTRODUCTION /546 11.2 FUNCTIONALS AND EXTREMALS / 547 11.3 SOME
CLASSICAL VARIATIONAL PROBLEMS / 552 11.4 VARIATIONAL NOTATION / 555
11.5 OTHER TYPES OF FUNCTIONALS / 559 11.6 ISOPERIMETRIC PROBLEMS / 564
11.7 RAYLEIGH-RITZ APPROXIMATION METHOD / 567 11.8 HAMILTON S PRINCIPLE
/ 572 11.9 STATIC EQUILIBRIUM OF DEFORMABLE BODIES / 579 11.10
TWO-DIMENSIONAL VARIATIONAL PROBLEMS /581 SUGGESTED READING / 584
EXERCISES /584 12 PARTIAL DIFFERENTIAL EQUATIONS / 589 12.1 INTRODUCTION
/591 12.2 CLASSIFICATION OF SECOND-ORDER PDES /591 12.3 THE HEAT
EQUATION /592 12.4 THE WAVE EQUATION / 600 12.5 THE EQUATION OF LAPLACE
/ 604 12.6 GENERALIZED FOURIER SERIES / 611 12.7 APPLICATIONS INVOLVING
BESSEL FUNCTIONS /617 12.8 TRANSFORM METHODS / 621 SUGGESTED READING /
631 EXERCISES / 632 13 PROBABILITY AND RANDOM VARIABLES / 637 13.1
INTRODUCTION /638 13.2 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS /
640 13.3 EXAMPLES OF DENSITY FUNCTIONS /646 13.4 EXPECTED VALUES /649
13.5 CONDITIONAL PROBABILITY / 655 13.6 FUNCTIONS OF ONE RANDOM VARIABLE
/ 658 13.7 TWO RANDOM VARIABLES /665 13.8 FUNCTIONS OF TWO OR MORE
RANDOM VARIABLES / 677 13.9 LIMIT DISTRIBUTIONS / 690 SUGGESTED READING
/ 692 EXERCISES /693 CONTENTS IX 14 RANDOM PROCESSES / 697 14.1
INTRODUCTION /698 14.2 PROBABILISTIC DESCRIPTION OF RANDOM PROCESS / 698
14.3 AUTOCORRELATION AND AUTOCOVARIANCE FUNCTIONS / 700 14.4
CROSS-CORRELATION AND CROSS-COVARIANCE / 708 14.5 POWER SPECTRAL DENSITY
FUNCTIONS / 711 14.6 TRANSFORMATIONS OF RANDOM PROCESSES /716 14.7
STATIONARY GAUSSIAN PROCESSES /722 SUGGESTED READING / 729 EXERCISES
/729 15 APPLICATIONS /733 15.1 INTRODUCTION /734 15.2 MECHANICAL
VIBRATIONS AND ELECTRIC CIRCUITS / 734 15.3 BUCKLING OF A LONG COLUMN /
742 15.4 COMMUNICATION SYSTEMS / 745 15.5 APPLICATIONS IN GEOMETRICAL
OPTICS / 756 15.6 WAVE PROPAGATION IN FREE SPACE / 762 15.7 ABCD
MATRICES FOR PARAXIAL SYSTEMS / 767 15.8 ZERNIKE POLYNOMIALS / 773
EXERCISES /780 REFERENCES /783 INDEX/ 785
|
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| illustrated | Illustrated |
| indexdate | 2024-12-20T11:04:46Z |
| institution | BVB |
| isbn | 0819445061 |
| language | English |
| lccn | 2002070783 |
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| series2 | SPIE press monograph |
| spellingShingle | Andrews, Larry C. Phillips, Ronald L. Mathematical techniques for engineers and scientists SPIE press monograph Análise matemática larpcal Engenharia larpcal Matemática aplicada larpcal Mathematical analysis Naturwissenschaften (DE-588)4041421-8 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4041421-8 (DE-588)4037944-9 (DE-588)4137304-2 (DE-588)4142443-8 |
| title | Mathematical techniques for engineers and scientists |
| title_auth | Mathematical techniques for engineers and scientists |
| title_exact_search | Mathematical techniques for engineers and scientists |
| title_full | Mathematical techniques for engineers and scientists Larry C. Andrews, Ronald L. Phillips |
| title_fullStr | Mathematical techniques for engineers and scientists Larry C. Andrews, Ronald L. Phillips |
| title_full_unstemmed | Mathematical techniques for engineers and scientists Larry C. Andrews, Ronald L. Phillips |
| title_short | Mathematical techniques for engineers and scientists |
| title_sort | mathematical techniques for engineers and scientists |
| topic | Análise matemática larpcal Engenharia larpcal Matemática aplicada larpcal Mathematical analysis Naturwissenschaften (DE-588)4041421-8 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Análise matemática Engenharia Matemática aplicada Mathematical analysis Naturwissenschaften Mathematik Ingenieurwissenschaften Angewandte Mathematik |
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