Advanced mathematics for engineering and science:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 880 S. graph. Darst. |
| ISBN: | 9812382917 |
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Record in the Search Index
| _version_ | 1804130210458632192 |
|---|---|
| adam_text | VANCED MATHEMATICS FOR ENGINEERIN -* ANC SCIENCE BY * F CHAN MAN FONG
D DE KEE TULANE UNIVERSITY, USA P N KALONI UNIVERSITY OF WINDSOR, CANADA
VFE WORLD SCIENTIFIC W L NEW JERSEY * LONDON * SI. SINGAPORE * HONG KONG
CONTENTS CHAPTER 1 REVIEW OF CALCULUS AND ORDINARY DIFFERENTIAL
EQUATIONS 1 1.1 FUNCTIONS OF ONE REAL VARIABLE 1 1.2 DERIVATIVES 3 MEAN
VALUE THEOREM 4 CAUCHY MEAN VALUE THEOREM 4 L HOPITAL S RULE 5 TAYLOR S
THEOREM 5 MAXIMUM AND MINIMUM 6 1.3 INTEGRALS 7 INTEGRATION BY PARTS 8
INTEGRATION BY SUBSTITUTION 9 INTEGRATION OF RATIONAL FUNCTIONS 10 1.4
FUNCTIONS OF SEVERAL VARIABLES 13 1.5 DERIVATIVES 13 TOTAL DERIVATIVES
16 1.6 IMPLICIT FUNCTIONS 19 1.7 SOME THEOREMS 21 EULER S THEOREM 21
TAYLOR S THEOREM 22 1.8 INTEGRAL OF A FUNCTION DEPENDING ON A PARAMETER
22 1.9 ORDINARY DIFFERENTIAL EQUATIONS (O.D.E.) - DEFINITIONS 25 1.10
FIRST-ORDER DIFFERENTIAL EQUATIONS 26 1.11 SEPARABLE FIRST-ORDER
DIFFERENTIAL EQUATIONS 26 1.12 HOMOGENEOUS FIRST-ORDER DIFFERENTIAL
EQUATIONS 27 1.13 TOTAL OR EXACT FIRST-ORDER DIFFERENTIAL EQUATIONS 31
1.14 LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 36 1.15 BERNOULLI S
EQUATION 39 1.16 SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH
CONSTANT COEFFICIENTS 41 1.17 SOLUTIONS BY LAPLACE TRANSFORM 46
HEAVISIDE STEP FUNCTION AND DIRAC DELTA FUNCTION 49 1.18 SOLUTIONS USING
GREEN S FUNCTIONS 57 1.19 MODELLING OF PHYSICAL SYSTEMS 65 PROBLEMS 74
CHAPTER 2 SERIES SOLUTIONS AND SPECIAL FUNCTIONS 89 2.1 DEFINITIONS 89
IDII ADVANCED MATHEMATICS 2.2 POWER SERIES 92 2.3 ORDINARY POINTS 95 2.4
REGULAR SINGULAR POINTS AND THE METHOD OF FROBENIUS 99 2.5 METHOD OF
VARIATION OF PARAMETERS 118 2.6 STURM LIOUVILLE PROBLEM 120 2.7 SPECIAL
FUNCTIONS 126 LEGENDRE S FUNCTIONS 126 BESSEL FUNCTIONS 134 MODIFIED
BESSEL S EQUATION 141 2.8 FOURIER SERIES 144 FOURIER INTEGRAL 158 2.9
ASYMPTOTIC SOLUTIONS 162 PARAMETER EXPANSION 170 PROBLEMS 179 CHAPTER 3
COMPLEX VARIABLES 191 3.1 INTRODUCTION 191 3.2 BASIC PROPERTIES OF
COMPLEX NUMBERS 192 3.3 COMPLEX FUNCTIONS 198 3.4 ELEMENTARY FUNCTIONS
213 3.5 COMPLEX INTEGRATION 220 CAUCHY S THEOREM 227 CAUCHY S INTEGRAL
FORMULA 233 INTEGRAL FORMULAE FOR DERIVATIVES 233 MORERA S THEOREM 237
MAXIMUM MODULUS PRINCIPLE 237 3.6 SERIES REPRESENTATIONS OF ANALYTIC
FUNCTIONS 238 TAYLOR SERIES 242 LAURENT SERIES 246 3.7 RESIDUE THEORY
253 CAUCHY S RESIDUE THEOREM 257 SOME METHODS OF EVALUATING THE RESIDUES
258 TRIGINOMETRIC INTEGRALS 263 IMPROPER INTEGRALS OF RATIONAL FUNCTIONS
265 EVALUATING INTEGRALS USING JORDAN S LEMMA 269 3.8 CONFORMAL MAPPING
275 LINEAR TRANSFORMATION 279 RECIPROCAL TRANSFORMATION 282 BILINEAR
TRANSFORMATION 284 SCHWARZ-CHRISTOFFEL TRANSFORMATION 287 CONTENTS *
JOUKOWSKI TRANSFORMATION 289 PROBLEMS 293 CHAPTER 4 VECTOR AND TENSOR
ANALYSIS 301 4.1 INTRODUCTION 301 4.2 VECTORS 301 4.3 LINE, SURFACE AND
VOLUME INTEGRALS 305 4.4 RELATIONS BETWEEN LINE, SURFACE AND VOLUME
INTEGRALS 327 GAUSS (DIVERGENCE) THEOREM 327 STOKES THEOREM 333 4.5
APPLICATIONS 336 CONSERVATION OF MASS 336 SOLUTION OF POISSON S EQUATION
338 NON-EXISTENCE OF PERIODIC SOLUTIONS 340 MAXWELL S EQUATIONS 341 4.6
GENERAL CURVILINEAR COORDINATE SYSTEMS AND HIGHER ORDER TENSORS 342
CARTESIAN VECTORS AND SUMMATION CONVENTION 342 GENERAL CURVILINEAR
COORDINATE SYSTEMS 347 TENSORS OF ARBITRARY ORDER 354 METRIC AND
PERMUTATION TENSORS 357 COVARIANT, CONTRAVARIANT AND PHYSICAL COMPONENTS
361 4.7 COVARIANT DIFFERENTIATION 366 PROPERTIES OF CHRISTOFFEL SYMBOLS
368 4.8 INTEGRAL TRANSFORMS 379 4.9 ISOTROPIC, OBJECTIVE TENSORS AND
TENSOR-VALUED FUNCTIONS 382 PROBLEMS 391 CHAPTER 5 PARTIAL DIFFERENTIAL
EQUATIONS I 401 5.1 INTRODUCTION 401 5.2 FIRST ORDER EQUATIONS 402
METHOD OF CHARACTERISTICS 402 LAGRANGE S METHOD 411 TRANSFORMATION
METHOD 414 5.3 SECOND ORDER LINEAR EQUATIONS 420 CLASSIFICATION 420 5.4
METHOD OF SEPARATION OF VARIABLES 427 WAVE EQUATION 427 D ALEMBERT S
SOLUTION 431 DIFFUSION EQUATION 435 LAPLACE S EQUATION 437 2L ADVANCED
MATHEMATICS 5.5 CYLINDRICAL AND SPHERICAL POLAR COORDINATE SYSTEMS 439
5.6 BOUNDARY AND INITIAL CONDITIONS 447 5.7 NON-HOMOGENEOUS PROBLEMS 450
5.8 LAPLACE TRANSFORMS 460 5.9 FOURIER TRANSFORMS 474 5.10 HANKEL AND
MELLIN TRANSFORMS 483 5.11 SUMMARY 494 PROBLEMS 496 CHAPTER 6 PARTIAL
DIFFERENTIAL EQUATIONS II 511 6.1 INTRODUCTION 511 6.2 METHOD OF
CHARACTERISTICS 511 6.3 SIMILARITY SOLUTIONS 523 6.4 GREEN S FUNCTIONS
532 DIRICHLET PROBLEMS 532 NEUMANN PROBLEMS 540 MIXED PROBLEMS (ROBIN S
PROBLEMS) 545 CONFORMAL MAPPING 547 6.5 GREEN S FUNCTIONS FOR GENERAL
LINEAR OPERATORS 548 6.6 QUANTUM MECHANICS 551 LIMITATIONS OF NEWTONIAN
MECHANICS 551 SCHROEDINGER EQUATION 552 PROBLEMS 562 CHAPTER 7 NUMERICAL
METHODS 569 7.1 INTRODUCTION 569 7.2 SOLUTIONS OF EQUATIONS IN ONE
VARIABLE 570 BISECTION METHOD (INTERNAL HALVING METHOD) 571 SECANT
METHOD 572 NEWTON S METHOD 574 FIXED POINT ITERATION METHOD 576 7.3
POLYNOMIAL EQUATIONS 580 NEWTON S METHOD 580 7.4 SIMULTANEOUS LINEAR
EQUATIONS 584 GAUSSIAN ELIMINATION METHOD 585 ITERATIVE METHOD 595 7.5
EIGENVALUE PROBLEMS 600 HOUSEHOLDER ALGORITHM 601 THE QR ALGORITHM 608
7.6 INTERPOLATION 611 CONTENTS -JLL LAGRANGE INTERPOLATION 611 NEWTON S
DIVIDED DIFFERENCE REPRESENTATION 614 SPLINE FUNCTIONS 619 LEAST SQUARES
APPROXIMATION 623 7.7 NUMERICAL DIFFERENTIATION AND INTEGRATION 625
NUMERICAL DIFFERENTIATION 625 NUMERICAL INTEGRATION 629 7.8 NUMERICAL
SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS, INITIAL VALUE PROBLEMS 637
FIRST ORDER EQUATIONS 638 EULER S METHOD 639 TAYLOR S METHOD 640 HEUN S
METHOD 643 RUNGE-KUTTA METHODS 643 ADAMS-BASHFORTH METHOD 646 HIGHER
ORDER OR SYSTEMS OF FIRST ORDER EQUATIONS 648 7.9 BOUNDARY VALUE
PROBLEMS 659 SHOOTING METHOD 659 FINITE DIFFERENCE METHOD 665 7.10
STABILITY 671 PROBLEMS 673 CHAPTER 8 NUMERICAL SOLUTION OF PARTIAL
DIFFERENTIAL EQUATIONS 681 8.1 INTRODUCTION 681 8.2 FINITE DIFFERENCES
681 8.3 PARABOLIC EQUATIONS 683 EXPLICIT METHOD 684 CRANK-NICOLSON
IMPLICIT METHOD 686 DERIVATIVE BOUNDARY CONDITIONS 690 8.4 ELLIPTIC
EQUATIONS 696 DIRICHLET PROBLEM 697 NEUMANN PROBLEM 701 POISSON S AND
HELMHOLTZ S EQUATIONS 703 8.5 HYPERBOLIC EQUATIONS 706 DIFFERENCE
EQUATIONS 706 METHOD OF CHARACTERISTICS 710 8.6 IRREGULAR BOUNDARIES AND
HIGHER DIMENSIONS 715 8.7 NON-LINEAR EQUATIONS 717 8.8 FINITE ELEMENTS
722 ONE-DIMENSIONAL PROBLEMS 722 VARIATIONAL METHOD 723 * ADVANCED
MATHEMATICS GALERKIN METHOD 724 TWO-DIMENSIONAL PROBLEMS 727 PROBLEMS
734 CHAPTER 9 CALCULUS OF VARIATIONS 739 9.1 INTRODUCTION 739 9.2
FUNCTION OF ONE VARIABLE 740 9.3 FUNCTION OF SEVERAL VARIABLES 742 9.4
CONSTRAINED EXTREMA AND LAGRANGE MULTIPLIERS 745 9.5 EULER-LAGRANGE
EQUATIONS 747 9.6 SPECIAL CASES 749 FUNCTION F DOES NOT DEPEND ON Y
EXPLICITLY 749 FUNCTION F DOES NOT DEPEND ON * EXPLICITLY 751 FUNCTION F
DOES NOT DEPEND ON X EXPLICITLY 752 FUNCTION F IS A LINEAR FUNCTION OF
Y 754 9.7 EXTENSION TO HIGHER DERIVATIVES 756 9.8 TRANSVERSALITY
(MOVING BOUNDARY) CONDITIONS 757 9.9 CONSTRAINTS 760 9.10 SEVERAL
DEPENDENT VARIABLES 765 9.11 SEVERAL INDEPENDENT VARIABLES 772 9.12
TRANSVERSALITY CONDITIONS WHERE THE FUNCTIONAL DEPENDS ON SEVERAL
FUNCTIONS 786 9.13 SUBSIDIARY CONDITIONS WHERE THE FUNCTIONAL DEPENDS ON
SEVERAL FUNCTIONS 790 PROBLEMS 803 CHAPTER 10 SPECIAL TOPICS 809 10.1
INTRODUCTION 809 10.2 PHASE SPACE 809 10.3 HAMILTON S EQUATIONS OF
MOTION 814 10.4 POISSON BRACKETS 817 10.5 CANONICAL TRANSFORMATIONS 819
10.6 LIOUVILLE S THEOREM 823 10.7 DISCRETE PROBABILITY THEORY 826 10.8
BINOMIAL, POISSON AND NORMAL DISTRIBUTION 830 10.9 SCOPE OF STATISTICAL
MECHANICS 840 10.10 BASIC ASSUMPTIONS 842 10.11 STATISTICAL
THERMODYNAMICS 845 10.12 THE EQUIPARTITION THEOREM 851 10.13 MAXWELL
VELOCITY DISTRIBUTION 852 10.14 *ROWNIAN MOTION 853 PROBLEMS 856
CONTENTS REFERENCES 861 APPENDICES 867 APPENDIX I - THE EQUATION OF
CONTINUITY IN SEVERAL COORDINATE SYSTEMS 867 APPENDIX II - THE EQUATION
OF MOTION IN SEVERAL COORDINATE SYSTEMS 868 APPENDIX III - THE EQUATION
OF ENERGY IN TERMS OF THE TRANSPORT PROPERTIES 871 IN SEVERAL COORDINATE
SYSTEMS APPENDIX IV - THE EQUATION OF CONTINUITY OF SPECIES A IN SEVERAL
COORDINATE SYSTEMS 873 AUTHOR INDEX 875 SUBJECT INDEX 877
|
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| indexdate | 2024-07-09T19:17:25Z |
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| isbn | 9812382917 |
| language | English |
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| spelling | Chen, Wenfang 1938- Verfasser (DE-588)124059325 aut Advanced mathematics for engineering and science by C. F. Chan Man Fong ; D. De Kee ; P. N. Kaloni New Jersey [u.a.] World Scientific 2003 XIII, 880 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Ingenieurwissenschaften (DE-588)4137304-2 s Mathematik (DE-588)4037944-9 s De Kee, Daniel 1949- Verfasser (DE-588)124059376 aut Kaloni, Purna N. Verfasser (DE-588)124059422 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010478325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Wenfang 1938- De Kee, Daniel 1949- Kaloni, Purna N. Advanced mathematics for engineering and science Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4037944-9 (DE-588)4137304-2 (DE-588)4143389-0 |
| title | Advanced mathematics for engineering and science |
| title_auth | Advanced mathematics for engineering and science |
| title_exact_search | Advanced mathematics for engineering and science |
| title_full | Advanced mathematics for engineering and science by C. F. Chan Man Fong ; D. De Kee ; P. N. Kaloni |
| title_fullStr | Advanced mathematics for engineering and science by C. F. Chan Man Fong ; D. De Kee ; P. N. Kaloni |
| title_full_unstemmed | Advanced mathematics for engineering and science by C. F. Chan Man Fong ; D. De Kee ; P. N. Kaloni |
| title_short | Advanced mathematics for engineering and science |
| title_sort | advanced mathematics for engineering and science |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Mathematische Physik Mathematik Ingenieurwissenschaften Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010478325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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