Holdings: Mathematical techniques

Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences

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Bibliographic Details
Main Authors:	Jordan, Dominic W. (Author), Smith, Peter 1935- (Author)
Format:	Book
Language:	English
Published:	Oxford [u.a.] Oxford Univ. Press 2002
Edition:	3. ed.
Subjects:	Mathematica > Programm Ingenieurwissenschaften Mathematische Physik Mathematik Aufgabensammlung
Online Access:	Inhaltsverzeichnis
Physical Description:	XVIII, 862 S. graph. Darst.
ISBN:	0199249725

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adam_text	MATHEMATICAL TECHNIQUES AN INTRODUCTION FOR THE ENGINEERING, PHYSICAL, AND MATHEMATICAL SCIENCES THDRE D. W. JORDAN AND P. SMITH DEPARTMENT OF MATHEMATICS KEELE UNIVERSITY OXFORD UNIVERSITY PRESS CONTENTS ART ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS 1 STANDARD FUNCTIONS AND TECHNIQUES 1.1 REAL NUMBERS, POWERS, INEQUALITIES 2 1.2 COORDINATES IN THE PLANE 4 1.3 GRAPHS 5 1.4 FUNCTIONS 8 1.5 RADIAN MEASURE OF ANGLES 11 1.6 TRIGONOMETRIC FUNCTIONS; PROPERTIES 12 1.7 INVERSE FUNCTIONS 16 1.8 INVERSE TRIGONOMETRIC FUNCTIONS 18 1.9 POLAR COORDINATES 21 1.10 EXPONENTIAL FUNCTIONS; THE NUMBER E 23 1.11 THE LOGARITHMIC FUNCTION 25 1.12 EXPONENTIAL GROWTH AND DECAY 27 1.13 HYPERBOLIC FUNCTIONS 29 1.14 PARTIAL FRACTIONS 31 1.15 SUMMATION SIGN: GEOMETRIC SERIES 35 1.16 INFINITE GEOMETRIC SERIES 37 1.17 PERMUTATIONS AND COMBINATIONS 39 1.18 THE BINOMIAL THEOREM 44 PROBLEMS 48 2 DIFFERENTIATION 57 THE SLOPE OF A GRAPH 54 THE DERIVATIVE: NOTATION AND DEFINITION RATES OF CHANGE 58 DERIVATIVE OF X ( = 0, L\| 2,3, ... ) 60 DERIVATIVES OF SUMS: MULTIPLICATION BY CONSTANTS THREE IMPORTANT LIMITS 63 DERIVATIVES OF E, SIN X, COS X, IN X 65 A BASIC TABLE OF DERIVATIVES 67 HIGHER-ORDER DERIVATIVES 68 62 70 FURTHER TECHNIQUES FOR DIFFERENTIATION 3.1 THE PRODUCT RULE 73 3.2 QUOTIENTS AND RECIPROCALS 75 3.3 THE CHAIN RULE 77 3.4 DERIVATIVE OF X FOR ANY VALUE OF N 80 3.5 FUNCTIONS OF AX + B 81 3.6 AN EXTENSION OF THE CHAIN RULE 82 3.7 LOGARITHMIC DIFFERENTIATION 82 CONTENTS PART II MATRIX ALGEBRA AND VECTORS 3.8 IMPLICIT DIFFERENTIATION 83 3.9 DERIVATIVES OF INVERSE FUNCTIONS 84 3.10 DERIVATIVE AS A FUNCTION OF A PARAMETER PROBLEMS 88 85 APPLICATIONS OF DIFFERENTIATION 4.1 FUNCTION NOTATION FOR DERIVATIVES 90 4.2 MAXIMA AND MINIMA 92 4.3 EXCEPTIONAL CASES OF MAXIMA AND MINIMA 96 4.4 SKETCHING GRAPHS OF FUNCTIONS 97 4.5 ESTIMATING SMALL CHANGES 102 4.6 NUMERICAL SOLUTION OF EQUATIONS: NEWTON S METHOD 104 4.7 THE BINOMIAL THEOREM 107 PROBLEMS 109 TAYLOR SERIES AND APPROXIMATIONS 5.1 THE INDEX NOTATION FOR DERIVATIVES OF ANY ORDER 111 5.2 TAYLOR POLYNOMIALS 111 5.3 A NOTE ON INFINITE SERIES 114 5.4 INFINITE TAYLOR EXPANSIONS 116 5.5 MANIPULATION OF TAYLOR SERIES 118 5.6 APPROXIMATIONS FOR LARGE VALUES OF X 120 5.7 TAYLOR SERIES ABOUT OTHER POINTS 121 5.8 INDETERMINATE VALUES; L HOPITAL S RULE 122 PROBLEMS 124 COMPLEX NUMBERS 6.1 DEFINITIONS AND RULES 126 6.2 THE ARGAND DIAGRAM AND COMPLEX NUMBERS 131 6.3 COMPLEX NUMBERS IN POLAR COORDINATES 132 6.4 COMPLEX NUMBERS IN EXPONENTIAL FORM 134 6.5 THE GENERAL EXPONENTIAL FORM 137 6.6 HYPERBOLIC FUNCTIONS 139 6.7 MISCELLANEOUS APPLICATIONS 140 PROBLEMS 141 MATRIX ALGEBRA 7.1 MATRIX DEFINITION AND NOTATION 144 7.2 RULES OF MATRIX ALGEBRA 145 7.3 SPECIAL MATRICES 151 7.4 THE INVERSE MATRIX 155 PROBLEMS 160 8 DETERMINANTS 8.1 THE DETERMINANT OF A SQUARE MATRIX 162 8.2 PROPERTIES OF DETERMINANTS 165 8.3 THE ADJOINT AND INVERSE MATRICES 170 PROBLEMS 172 CONTENTS 9 ELEMENTARY OPERATIONS WITH VECTORS 9.1 DISPLACEMENT ALONG AN AXIS 175 9.2 DISPLACEMENT VECTORS IN TWO DIMENSIONS 177 9.3 AXES IN THREE DIMENSIONS 179 9.4 VECTORS IN TWO AND THREE DIMENSIONS 179 9.5 RELATIVE VELOCITY 183 9.6 POSITION VECTORS AND VECTOR EQUATIONS 185 9.7 UNIT VECTORS AND BASIS VECTORS 189 9.8 TANGENT VECTOR, VELOCITY, AND ACCELERATION 190 9.9 MOTION IN POLAR COORDINATES 192 PROBLEMS 193 10 THE SCALAR PRODUCT 10.1 THE SCALAR PRODUCT OF TWO VECTORS 196 10.2 THE ANGLE BETWEEN TWO VECTORS 197 10.3 PERPENDICULAR VECTORS 198 10.4 ROTATION OF AXES IN TWO DIMENSIONS 200 10.5 DIRECTION COSINES 200 10.6 ROTATION OF AXES IN THREE DIMENSIONS 202 10.7 DIRECTION RATIOS AND COORDINATE GEOMETRY 204 10.8 PROPERTIES OF A PLANE 205 10.9 GENERAL EQUATION OF A STRAIGHT LINE 208 10.10 FORCES ACTING AT A POINT 209 10.11 CURVATURE IN TWO DIMENSIONS 211 PROBLEMS 213 11 VECTOR PRODUCT 11.1 VECTOR PRODUCT 216 11.2 NATURE OF THE VECTOR P = A X B 217 11.3 THE SCALAR TRIPLE PRODUCT 220 11.4 MOMENT OF A FORCE 222 11.5 VECTOR TRIPLE PRODUCT 225 PROBLEMS 226 12 LINEAR ALGEBRAIC EQUATIONS 12.1 CRAMER S RULE 229 12.2 ELEMENTARY ROW OPERATIONS 232 12.3 THE INVERSE MATRIX BY GAUSSIAN ELIMINATION 235 12.4 COMPATIBLE AND INCOMPATIBLE SETS OF EQUATIONS 236 12.5 HOMOGENEOUS SETS OF EQUATIONS 240 12.6 GAUSS-SEIDEL ITERATIVE METHOD OF SOLUTION 242 PROBLEMS 245 13 EIGENVALUES AND EIGENVECTORS 13.1 EIGENVALUES OF A MATRIX 248 13.2 EIGENVECTORS 250 13.3 LINEAR DEPENDENCE 254 13.4 DIAGONALIZATION OF A MATRIX 256 CONTENTS PART III INTEGRATION AND DIFFERENTIAL EQUATIONS 13.5 POWERS OF MATRICES 259 13.6 QUADRATIC FORMS 262 13.7 POSITIVE-DEFINITE MATRICES 264 13.8 AN APPLICATION TO A VIBRATING SYSTEM PROBLEMS 270 267 14 ANTIDIFFERENTIATION AND AREA 14.1 REVERSING DIFFERENTIATION 274 14.2 CONSTRUCTING A TABLE OF ANTIDERIVATIVES 14.3 SIGNED AREA GENERATED BY A GRAPH 280 PROBLEMS 282 278 285 15 THE DEFINITE AND INDEFINITE INTEGRAL 15.1 SIGNED AREA AS THE SUM OF STRIPS 284 15.2 NUMERICAL ILLUSTRATION OF THE SUM FORMULA 15.3 THE DEFINITE INTEGRAL AND AREA 286 15.4 THE INDEFINITE-INTEGRAL NOTATION 287 15.5 INTEGRALS UNRELATED TO AREA 289 15.6 IMPROPER INTEGRALS 291 15.7 INTEGRATION OF COMPLEX FUNCTIONS: A NEW TYPE OF INTEGRAL 15.8 THE AREA ANALOGY FOR A DEFINITE INTEGRAL 295 15.9 SYMMETRIC INTEGRALS 296 293 298 16 APPLICATIONS INVOLVING THE INTEGRAL AS A SUM 16.1 EXAMPLES OF INTEGRALS ARISING FROM A SUM 302 16.2 GEOMETRICAL AREA IN POLAR COORDINATES 304 16.3 THE TRAPEZIUM RULE 305 16.4 CENTRE OF MASS, MOMENT OF INERTIA 307 PROBLEMS 311 17 SYSTEMATIC TECHNIQUES FOR INTEGRATION 17.1 SUBSTITUTION METHOD FOR J F(AX + B) DX 314 17.2 SUBSTITUTION METHOD FOR J F(AX 2 + B)X DX 316 17.3 SUBSTITUTION METHOD FOR J COS M AX SIN AX DX (M OR N ODD) 318 17.4 DEFINITE INTEGRALS AND CHANGE OF VARIABLE 320 17.5 OCCASIONAL SUBSTITUTIONS 321 17.6 PARTIAL FRACTIONS FOR INTEGRATION 323 17.7 INTEGRATION BY PARTS 325 17.8 INTEGRATION BY PARTS: DEFINITE INTEGRALS 328 1 7.9 DIFFERENTIATING WITH RESPECT TO A PARAMETER 331 PROBLEMS 332 18 UNFORCED LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 18.1 DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS 336 18.2 SOLVING FIRST-ORDER LINEAR UNFORCED EQUATIONS 339 CONTENTS 18.3 SOLVING SECOND-ORDER LINEAR UNFORCED EQUATIONS 342 18.4 COMPLEX ROOTS OF THE CHARACTERISTIC EQUATION 345 18.5 INITIAL CONDITIONS FOR SECOND-ORDER EQUATIONS 348 PROBLEMS 349 19 FORCED LINEAR DIFFERENTIAL EQUATIONS 19.1 PARTICULAR SOLUTIONS FOR STANDARD FORCING TERMS 351 19.2 HARMONIC FORCING TERM BY USING COMPLEX SOLUTIONS 355 19.3 PARTICULAR SOLUTIONS: EXCEPTIONAL CASES 358 19.4 THE GENERAL SOLUTION OF FORCED EQUATIONS 360 19.5 FIRST-ORDER LINEAR EQUATIONS WITH A VARIABLE COEFFICIENT 363 PROBLEMS 366 20 HARMONIC FUNCTIONS AND THE HARMONIC OSCILLATOR 20.1 HARMONIC OSCILLATIONS 368 20.2 PHASE DIFFERENCE: LEAD AND LAG 370 20.3 PHYSICAL MODELS OF A DIFFERENTIAL EQUATION 371 20.4 FREE OSCILLATIONS OF A LINEAR OSCILLATOR 372 20.5 FORCED OSCILLATIONS AND TRANSIENTS 373 20.6 RESONANCE 376 20.7 NEARLY LINEAR SYSTEMS 378 20.8 STATIONARY AND TRAVELLING WAVES 380 20.9 COMPOUND OSCILLATIONS; BEATS 384 20.10 TRAVELLING WAVES; BEATS 387 20.11 DISPERSION; GROUP VELOCITY 388 20.12 THE DOPPLER EFFECT 390 PROBLEMS 391 21 STEADY FORCED OSCILLATIONS: PHASORS, IMPEDANCE, TRANSFER FUNCTIONS 21.1 PHASORS 394 21.2 ALGEBRA OF PHASORS 396 21.3 PHASOR DIAGRAMS 397 21.4 PHASORS AND COMPLEX IMPEDANCE 398 21.5 TRANSFER FUNCTIONS IN THE FREQUENCY DOMAIN 402 21.6 PHASORS AND WAVES; COMPLEX AMPLITUDE 404 PROBLEMS 408 22 GRAPHICAL, NUMERICAL, AND OTHER ASPECTS OF FIRST-ORDER EQUATIONS 22.1 GRAPHICAL FEATURES OF FIRST-ORDER EQUATIONS 410 22.2 THE EULER METHOD FOR NUMERICAL SOLUTION 412 22.3 NONLINEAR EQUATIONS OF SEPARABLE TYPE 414 22.4 DIFFERENTIALS AND THE SOLUTION OF FIRST-ORDER EQUATIONS 417 22.5 CHANGE OF VARIABLE IN A DIFFERENTIAL EQUATION 421 PROBLEMS ( 424 CONTENTS PART IV TRANSFORMS AND FOURIER SERIES 23 NONLINEAR DIFFERENTIAL EQUATIONS AND THE PHASE PLANE 23.1 AUTONOMOUS SECOND-ORDER EQUATIONS 429 23.2 CONSTRUCTING A PHASE DIAGRAM FOR (X, X) 430 23.3 (X, X) PHASE DIAGRAMS FOR OTHER LINEAR EQUATIONS; STABILITY 433 23.4 THE PENDULUM EQUATION 436 23.5 THE GENERAL PHASE PLANE 438 23.6 APPROXIMATE LINEARIZATION 441 23.7 LIMIT CYCLES 442 23.8 A NUMERICAL METHOD FOR PHASE PATHS 443 PROBLEMS 445 24 THE LAPLACE TRANSFORM 24.1 THE LAPLACE TRANSFORM 448 24.2 LAPLACE TRANSFORMS OF T , E* , SIN T, COS T 449 24.3 SCALE RULE; SHIFT RULE; FACTORS T AND E KL 451 24.4 INVERTING A LAPLACE TRANSFORM 455 24.5 LAPLACE TRANSFORMS OF DERIVATIVES 457 24.6 APPLICATION TO DIFFERENTIAL EQUATIONS 458 24.7 THE UNIT FUNCTION AND THE DELAY RULE 461 PROBLEMS 465 25 LAPLACE AND Z TRANSFORMS: APPLICATIONS 467 473 DIVISION BY S AND INTEGRATION THE IMPULSE FUNCTION 469 IMPEDANCE IN THE S DOMAIN 471 TRANSFER FUNCTIONS IN THE S DOMAIN THE CONVOLUTION THEOREM 479 GENERAL RESPONSE OF A SYSTEM FROM ITS IMPULSIVE RESPONSE CONVOLUTION INTEGRAL IN TERMS OF MEMORY 482 DISCRETE SYSTEMS 483 THE Z TRANSFORM 485 25.10 BEHAVIOUR OF Z TRANSFORMS IN THE COMPLEX PLANE 490 25.11 Z TRANSFORMS AND DIFFERENCE EQUATIONS 494 PROBLEMS 496 26 FOURIER SERIES 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 481 THE COMPOSITION OF VIBRATIONS 500 FOURIER SERIES FOR A PERIODIC FUNCTION 501 INTEGRALS OF PERIODIC FUNCTIONS 502 CALCULATING THE FOURIER COEFFICIENTS 504 EXAMPLES OF FOURIER SERIES 506 USE OF SYMMETRY: SINE AND COSINE SERIES 509 FUNCTIONS DEFINED ON A FINITE RANGE: HALF-RANGE SERIES SPECTRUM OF A PERIODIC FUNCTION 513 OBTAINING ONE FOURIER SERIES FROM ANOTHER 514 515 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 26.10 THE TWO-SIDED FOURIER SERIES PROBLEMS 518 511 CONTENTS PART V MULTIVARIABLE CALCULUS 27 FOURIER TRANSFORMS 27.1 SINE AND COSINE TRANSFORMS 522 27.2 THE EXPONENTIAL FOURIER TRANSFORM 526 27.3 SHORT NOTATIONS: ALTERNATIVE EXPRESSIONS 527 27.4 FOURIER TRANSFORMS OF SOME BASIC FUNCTIONS 528 27.5 RULES FOR MANIPULATING TRANSFORMS 530 27.6 THE DELTA FUNCTION AND PERIODIC FUNCTIONS 533 27.7 CONVOLUTION THEOREM FOR FOURIER TRANSFORMS 535 27.8 THE SHAH FUNCTION 539 27.9 ENERGY IN A SIGNAL: RAYLEIGH S THEOREM 540 27.10 DIFFRACTION FROM A UNIFORMLY RADIATING STRIP 541 27.11 GENERAL SOURCE DISTRIBUTION AND THE INVERSE TRANSFORM 545 27.12 TRANSFORMS IN RADIATION PROBLEMS 546 PROBLEMS 550 28 DIFFERENTIATION OF FUNCTIONS OF TWO VARIABLES 28.1 FUNCTIONS OF MORE THAN ONE VARIABLE 553 28.2 DEPICTION OF FUNCTIONS OF TWO VARIABLES 554 28.3 PARTIAL DERIVATIVES 556 28.4 HIGHER DERIVATIVES 559 28.5 TANGENT PLANE AND NORMAL TO A SURFACE 562 28.6 MAXIMA, MINIMA, AND OTHER STATIONARY POINTS 564 28.7 THE METHOD OF LEAST SQUARES 567 28.8 DIFFERENTIATING AN INTEGRAL WITH RESPECT TO A PARAMETER 569 PROBLEMS 570 29 FUNCTIONS OF TWO VARIABLES: GEOMETRY AND FORMULAE 29.1 THE INCREMENTAL APPROXIMATION 573 29.2 SMALL CHANGES AND ERRORS 575 29.3 THE DERIVATIVE IN ANY DIRECTION 578 29.4 IMPLICIT DIFFERENTIATION 581 29.5 NORMAL TO A CURVE 584 29.6 GRADIENT VECTOR IN TWO DIMENSIONS 585 PROBLEMS 588 30 CHAIN RULES, RESTRICTED MAXIMA, COORDINATE SYSTEMS 30.1 CHAIN RULE FOR A SINGLE PARAMETER 590 30.2 RESTRICTED MAXIMA AND MINIMA: THE LAGRANGE MULTIPLIER 592 30.3 CURVILINEAR COORDINATES IN TWO DIMENSIONS 598 30.4 ORTHOGONAL COORDINATES 600 30.5 THE CHAIN RULE FOR TWO PARAMETERS 601 30.6 THE USE OF DIFFERENTIALS 604 PROBLEMS 606 31 FUNCTIONS OF ANY NUMBER OF VARIABLES 31.1 THE INCREMENTAL APPROXIMATION; ERRORS 608 31.2 IMPLICIT DIFFERENTIATION 610 CONTENTS 31.3 CHAIN RULES 612 31.4 THE GRADIENT VECTOR IN THREE DIMENSIONS 613 31.5 NORMAL TO A SURFACE 615 31.6 EQUATION OF THE TANGENT PLANE 616 31.7 DIRECTIONAL DERIVATIVE IN TERMS OF GRADIENT 616 31.8 STATIONARY POINTS 619 31.9 THE ENVELOPE OF A FAMILY OF CURVES 625 PROBLEMS 626 32 DOUBLE INTEGRATION 32.1 REPEATED INTEGRALS WITH CONSTANT LIMITS 630 32.2 EXAMPLES LEADING TO REPEATED INTEGRALS WITH CONSTANT LIMITS 632 32.3 REPEATED INTEGRALS OVER NON-RECTANGULAR REGIONS 634 32.4 CHANGING THE ORDER OF INTEGRATION FOR NON-RECTANGULAR REGIONS 636 32.5 DOUBLE INTEGRALS 637 32.6 POLAR COORDINATES 640 32.7 SEPARABLE INTEGRALS 643 32.8 GENERAL CHANGE OF VARIABLE; THE JACOBIAN DETERMINANT 645 PROBLEMS 649 33 LINE INTEGRALS PART VI DISCRETE MATHEMATICS ILLUSTRATING A LINE INTEGRAL 652 GENERAL LINE INTEGRALS IN TWO AND THREE DIMENSIONS PATHS PARALLEL TO THE AXES 659 PATH INDEPENDENCE AND PERFECT DIFFERENTIALS 659 CLOSED PATHS 661 GREEN S THEOREM 663 LINE INTEGRALS AND WORK 665 CONSERVATIVE FIELDS 667 POTENTIAL FOR A CONSERVATIVE FIELD 669 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 33.10 SINGLE-VALUEDNESS OF POTENTIALS PROBLEMS 673 655 670 34 VECTOR FIELDS: DIVERGENCE AND CURL 34.1 VECTOR FIELDS AND FIELD LINES 676 34.2 DIVERGENCE OF A VECTOR FIELD 677 34.3 SURFACE AND VOLUME INTEGRALS 678 34.4 THE DIVERGENCE THEOREM 682 34.5 CURL OF A VECTOR FIELD 684 34.6 CYLINDRICAL POLAR COORDINATES 688 34.7 CURVILINEAR COORDINATES 690 PROBLEMS 692 35 SETS 35.1 NOTATION 694 35.2 EQUALITY, UNION, AND INTERSECTION 35.3 VENN DIAGRAMS 697 PROBLEMS 702 695 CONTENTS 36 BOOLEAN ALGEBRA: LOGIC GATES AND SWITCHING FUNCTIONS 36.1 LAWS OF BOOLEAN ALGEBRA 705 36.2 LOGIC GATES AND TRUTH TABLES 707 36.3 LOGIC NETWORKS 709 36.4 THE INVERSE TRUTH-TABLE PROBLEM 711 36.5 SWITCHING CIRCUITS 712 PROBLEMS 714 37 GRAPH THEORY AND ITS APPLICATIONS 37.1 EXAMPLES OF GRAPHS 717 37.2 DEFINITIONS AND PROPERTIES OF GRAPHS 718 37.3 HOW MANY SIMPLE GRAPHS ARE THERE? 720 37.4 PATHS AND CYCLES 721 37.5 TREES 722 37.6 ELECTRICAL CIRCUITS: THE CUTSET METHOD 723 37.7 SIGNAL-FLOW GRAPHS 726 37.8 PLANAR GRAPHS 729 37.9 FURTHER APPLICATIONS 731 PROBLEMS 734 38 DIFFERENCE EQUATIONS 38.1 DISCRETE VARIABLES 739 - 38.2 DIFFERENCE EQUATIONS: GENERAL PROPERTIES 742 38.3 FIRST-ORDER DIFFERENCE EQUATIONS AND THE COBWEB 743 38.4 CONSTANT-COEFFICIENT LINEAR DIFFERENCE EQUATIONS 744 38.5 THE LOGISTIC DIFFERENCE EQUATION 750 PROBLEMS 754 PART VII PROBABILITY AND STATISTICS 39 PROBABILITY 39.1 INTRODUCTION 757 39.2 SAMPLE SPACES, EVENTS, AND PROBABILITY 39.3 SETS AND PROBABILITY 760 39.4 FREQUENCIES AND COMBINATIONS 764 39.5 CONDITIONAL PROBABILITY 767 39.6 INDEPENDENT EVENTS 769 39.7 TOTAL PROBABILITY 770 39.8 BAYES THEOREM 771 PROBLEMS 773 758 40 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 40.1 RANDOM VARIABLES 775 40.2 PROBABILITY DISTRIBUTIONS 776 40.3 THE BINOMIAL DISTRIBUTION 777 40.4 EXPECTED VALUE AND VARIANCE 779 40.5 GEOMETRIC DISTRIBUTION 782 40.6 POISSON DISTRIBUTION 783 40.7 OTHER DISCRETE DISTRIBUTIONS 785 CONTENTS 40.8 CONTINUOUS RANDOM VARIABLES AND DISTRIBUTIONS 786 40.9 MEAN AND VARIANCE OF CONTINUOUS RANDOM VARIABLES 788 40.10 THE NORMAL DISTRIBUTION 789 PROBLEMS 791 PART PROJECTS 41 DESCRIPTIVE STATISTICS 41.1 REPRESENTING DATA 793 41.2 RANDOM SAMPLES AND SAMPLING DISTRIBUTIONS 798 41.3 SAMPLE MEAN AND VARIANCE, AND HEIR ESTIMATION 799 41.4 CENTRAL LIMIT THEOREM 801 41.5 REGRESSION 803 PROBLEMS 805 42 APPLICATIONS PROJECTS USING SYMBOLIC COMPUTING 42.1 SYMBOLIC COMPUTATION 807 42.2 PROJECTS 808 ANSWERS TO SELECTED PROBLEMS 83I APPENDICES 842 A SOME ALGEBRAICAL RULES 842 B TRIGONOMETRIC FORMULAE 844 C AREAS AND VOLUMES 845 D A TABLE OF DERIVATIVES 846 E A TABLE OF INTEGRALS 847 F LAPLACE TRANSFORMS, INVERSES, AND GENERAL RULES 848 C EXPONENTIAL FOURIER TRANSFORMS AND RULES 849 H PROBABILITY DISTRIBUTIONS AND TABLES 850 INDEX 852
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genre_facet	Aufgabensammlung
id	DE-604.BV014184141
illustrated	Illustrated
indexdate	2024-07-09T18:59:09Z
institution	BVB
isbn	0199249725
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009722015
oclc_num	248467828
open_access_boolean
owner	DE-703 DE-634
owner_facet	DE-703 DE-634
physical	XVIII, 862 S. graph. Darst.
publishDate	2002
publishDateSearch	2002
publishDateSort	2002
publisher	Oxford Univ. Press
record_format	marc
spelling	Jordan, Dominic W. Verfasser (DE-588)115172602 aut Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith 3. ed. Oxford [u.a.] Oxford Univ. Press 2002 XVIII, 862 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s Ingenieurwissenschaften (DE-588)4137304-2 s DE-604 Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 Mathematica Programm (DE-588)4268208-3 s 3\p DE-604 Smith, Peter 1935- Verfasser (DE-588)141762349 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009722015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Jordan, Dominic W. Smith, Peter 1935- Mathematical techniques an introduction for the engineering, physical, and mathematical sciences Mathematica Programm (DE-588)4268208-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4268208-3 (DE-588)4137304-2 (DE-588)4037952-8 (DE-588)4037944-9 (DE-588)4143389-0
title	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences
title_auth	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences
title_exact_search	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences
title_full	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith
title_fullStr	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith
title_full_unstemmed	Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith
title_short	Mathematical techniques
title_sort	mathematical techniques an introduction for the engineering physical and mathematical sciences
title_sub	an introduction for the engineering, physical, and mathematical sciences
topic	Mathematica Programm (DE-588)4268208-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Mathematica Programm Ingenieurwissenschaften Mathematische Physik Mathematik Aufgabensammlung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009722015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT jordandominicw mathematicaltechniquesanintroductionfortheengineeringphysicalandmathematicalsciences AT smithpeter mathematicaltechniquesanintroductionfortheengineeringphysicalandmathematicalsciences

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