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Applied mathematics with Maple:

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Bibliographic Details
Main Author:	Andersson, Göran (Author)
Format:	Book
Language:	English
Published:	[Bromley u.a.] Chartwell-Bratt [u.a.] 1997
Subjects:	Maple V 4.0
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008459918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	448 S. Ill., graph. Darst.
ISBN:	0862384907 9144001495

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Record in the Search Index

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adam_text	GORAN ANDERSSON APPLIED MATHEMATICS WITH MAPLE SUB GOTTINGEN 210 075 724 99 A 4489 ) STUDENTLITTERATUR & CHARTWELL-BRATT CONTENTS PREFACE 11 1 INTRODUCTION 1.1 LIQUOR PROHIBITION 13 1.2 SECOND THOUGHTS 14 1.3 COLLISION PROBLEM 15 1.4 LOAN SHARKING 16 1.5 OIL TANK 18 2 MINI MANUAL 2.1 OPENING 21 2.2 MAPLE S USER INTERFACE 21 2.3 INPUT AND COMPUTATION 22 2.4 ELEMENTARY SYNTAX 24 2.4.1 STATEMENTS END WITH A SEMICOLON 24 2.4.2 MULTIPLICATION * 24 2.4.3 POWERS A 24 2.4.4 PREVIOUS RESULT IS WRITTEN 25 2.4.5 ASSIGNMENT := 25 2.4.6 FULL EVALUATION 26 2.4.7 SUPRESSED OUTPUT: 29 2.4.8 SUBSTITUTION 30 2.4.9 NUMERICAL RESULT 30 2.5 FUNCTIONS 31 2.5.1 DEFINING A FUNCTION 31 2.5.2 LIBRARIES AND PACKAGES 33 2.5.3 INERT FUNCTIONS 34 2.5.4 PROCEDURES 35 2.6 HELP 40 2.6.1 HELP MENU 40 2.6.2 HELP AT COMMAND LEVEL 40 2.7 SEQUENCES, LISTS AND SETS 42 2.7.1 OPENING 42 2.7.2 SEQUENCES 43 2.7.3 LISTS 45 2.7.4 SETS 49 2.7.5 TABLES AND ARRAYS 50 2.8 CONTROL FLOW 52 2.9 SHORT ABOUT FILES 55 2.10 2D GRAPHICS 56 2.10.1 OPENING 56 2.10.2 PLOTS OF FUNCTIONS 56 2.10.3 PLOTS OF DATA 59 2.11 3D GRAPHICS 60 2.11.1 PLOTS OF FUNCTIONS 60 2.11.2 PLOTS OF DATA 63 3 ALGEBRA 3.1 INTRODUCTION 65 3.2 ALGEBRAIC EXPRESSIONS 65 3.2.1 SIMPLIFICATION 65 3.2.2 REDUCING FRACTIONS 66 3.2.3 EXPANSION 67 3.2.4 FACTORING 67 3.2.5 RATIONAL EXPRESSIONS 68 3.2.6 PARTIAL FRACTIONS 69 3.2.7 SUBSTITUTION 69 3.3 POLYNOMIALS 70 3.3.1 DEGREE 70 3.3.2 FACTORING 74 3.3.3 COMPLETING THE SQUARE 78 3.4 SOLVING EQUATIONS 79 3.4.1 LINEAR EQUATION 79 3.4.2 QUADRATIC EQUATION 80 3.4.3 UNSOLVABLE 82 3.4.4 EQUATION WITH SQUARE ROOT 83 3.4.5 EQUATION WITH PARAMETER 83 3.4.6 COMPLEX ROOTS 84 3.4.7 CUBIC EQUATION 84 3.4.8 SYSTEM OF EQUATIONS 87 3.4.9 ELIMINATION 89 3.4.10 SYSTEM WITH PARAMETER 90 3.4.11 ABSOLUTE VALUE 91 LOGIC AND INTEGERS 4.1 OPENING 93 4.2 LOGIC 93 4.2.1 TRUE OR FALSE 93 4.2.2 AN EQUIVALENCE PROBLEM 96 4.2.3 DILEMMA 101 4.3 BOOLEAN ALGEBRA 105 4.3.1 DEFINITION 105 4.3.2 SOME BOOLEAN SIMPLIFICATIONS 107 4.3.3 BINARY NUMBERS 109 4.4 INTEGERS AND RATIONALS 112 4.4.1 AN ENORMOUS NUMBER 112 4.4.2 A PROBLEM WITH PRIMES 115 4.4.3 PERIOD OF 1/1994 116 4.4.4 HOW OLD IS THE PRIEST? 122 COMPLEX NUMBERS 5.1 OPENING 131 5.2 BASICS 131 5.2.1 THE FORM A+BI 131 5.2.2 CONJUGATE 132 5.2.3 ABSOLUTE VALUE 133 5.2.4 ARGUMENT 133 5.2.5 REAL SYMBOLS 135 5.3 COMPLEX PLANE 136 5.3.1 GRAPHING COMPLEX NUMBERS 136 5.3.2 THE FOUR RULES OF ARITHMETIC 143 5.3.3 TREASURE HUNTING 147 5.3.4 ANIMATION 150 5.3.5 LINES AND CIRCLES 154 5.4 EQUATIONS 156 5.4.1 REAL COEFFICIENTS 156 5.4.2 COMPLEX COEFFICIENTS 157 5.4.3 BINOMIC EQUATION 158 5.4.4 WHERE TO BUILD A SPORTS ARENA 161 5.5 COMPLEX MAPPINGS 164 5.5.1 THE MAPPING W = V Z 165 5.5.2 THE JOUKOWSKI AIRFOIL 171 5.5.3 A BEAUTIFUL EXAMPLE 173 6 VECTORS 6.1 OPENING 175 6.2 BASICS 175 6.2.1 ADDITION 175 6.2.2 SCALAR PRODUCT 178 6.2.3 VECTOR PRODUCT 181 6.3 THE LINE AND THE PLANE 184 6.3.1 LINE IN 2D 184 6.3.2 LINE AND PLANE IN 3D 187 6.4 THREE-DIMENSIONAL ILLUSION 194 6.4.1 CENTRAL PROJECTION 194 6.4.2 BASE VECTORS 196 6.4.3 PROJECTION OF THE UNIT CUBE 197 6.4.4 3D-PICTURE WITH COLOR 199 6.4.5 THE CUBE IN 3D 201 6.4.6 RANDOM PICTURE IN 3D 204 7 LINEAR ALGEBRA 7.1 OPENING 219 7.2 SYSTEMS OF LINEAR EQUATIONS 219 7.2.1 KIRCHHOFFS LAWS 219 7.2.2 TRAFFIC FLOW 224 7.3 MATRIX ALGEBRA 226 7.3.1 BASICS 226 7.3.2 A SYSTEM OF LINEAR EQUATIONS 231 7.3.3 A SYSTEM WITH A PARAMETER 232 7.3.4 GRAPHICS WITH MATRICES 234 7.3.5 OVER-DETERMINED SYSTEM OF EQUATIONS 240 7.3.6 EIGENVALUES AND EIGENVECTORS 244 8 CALCULUS 8.1 OPENING 247 8.2 ELEMENTARY FUNCTIONS 247 8.2.1 TRIGONOMETRIC FUNCTIONS 247 8.2.2 THE EXPONENTIAL AND THE NATURAL LOGARITHM 252 8.2.3 A SINE WAVE 253 8.3 LIMITS 254 8.3.1 A WELL-KNOWN LIMIT 254 8.3.2 A DISCONTINUOUS FUNCTION 255 8.4 DERIVATIVE 257 8.4.1 DEFINITION OF THE DERIVATAIVE 257 8.4.2 A FEW DERIVATIVES 260 8.4.3 THE EQUATION OF THE TANGENT LINE 264 8.4.4 NEWTON S METHOD 266 8.4.5 IMPLICIT DERIVATIVE 269 8.4.6 RADIUS OF CURVATURE 271 8.5 INTEGRALS 276 8.5.1 INDEFINITE INTEGRAL 276 8.5.2 DEFINITE INTEGRAL IN TWO WAYS 279 8.5.3 AN AREA 284 8.5.4 IMPROPER INTEGRALS 285 8.5.5 OIL TANK (AGAIN) 286 8.5.6 THE LENGTH OF A CURVE 290 8.5.7 A DOUBLE INTEGRAL 292 8.6 TAYLOR S FORMULA 297 8.6.1 EXPANSION OF/(X) 297 8.6.2 TAYLOR SERIES EXPANSION OF SIN X 298 8.6.3 HOW MANY TERMS? 300 8.7 FOURIER ANALYSIS 302 8.7.1 OPENING 302 8.7.2 TRIGONOMETRIC FOURIER SERIES 302 8.7.3 AMPLITUDE AND PHASE 307 8.7.4 COMPLEX REPRESENTATION 313 8.7.5 FOURIER TRANSFORM 316 8.8 FUNCTION FIT 318 8.8.1 IQ AND PERMILLAGE 318 9 DIFFERENTIAL EQUATIONS 9.1 OPENING 325 9.2 ORDINARY DE OF 1ST ORDER 325 9.2.1 INTRODUCTORY EXAMPLE 325 9.2.2 STEP AND IMPULSE FUNCTIONS 328 9.2.3 A SYSTEM OF DE S 329 9.2.4 NUMERICAL SOLUTION 331 9.2.5 DIRECTION FIELD 335 9.2.6 ADVANCED DE 337 9.3 ORDINARY DE OF HIGHER ORDER 338 9.3.1 LINEAR DE WITH CONSTANT COEFFICIENTS 338 9.3.2 LAPLACE TRANSFORM 340 9.3.3 LINEAR DE WITH VARIABLE COEFFICIENTS 345 9.4 APPLICATIONS 346 9.4.1 PROJECTILE FLIGHT WITHOUT FRICTION 346 9.4.2 PROJECTILE FLIGHT WITH FRICTION 351 9.4.3 PLANETARY MOTION 356 10 SEQUENCES AND SERIES 10.1 OPENING 363 10.2 REAL SEQUENCES 363 10.2.1 LOAN SHARKING (AGAIN) 363 10.2.2 GOLDEN RATIO AND FIBONACCI SEQUENCE 366 10.2.3 FEIGENBAUM 371 10.3 COMPLEX SEQUENCES 381 10.3.1 IMAGINARY POWER 381 10.3.2 MANDELBROT AND JULIA 383 11 PROBABILITY AND STATISTICS 11.1 OPENING 391 11.2 BASICS 391 11.2.1 BRIDGE 391 11.2.2 MIDSUMMER FLOWERS 393 11.3 DISCRETE RANDOM VARIABLES 395 11.3.1 DEFECTIVE COMPONENTS 395 11.3.2 RANDOM NUMBERS 398 11.4 CONTINUOUS RANDOM VARIABLES 403 11.4.1 NORMAL DISTRIBUTION 403 11.4.2 RANDOM NUMBERS 405 11.5 APPLICATIONS 408 11.5.1 BALL BEARINGS 408 11.5.2 LIGHT BULBS 409 11.5.3 DICE PROBLEM 413 11.6 STATISTICS 418 11.6.1 EXPERIMENT ON POINT ESTIMATE 418 11.6.2 EXPERIMENT ON CONFIDENCE INTERVAL 420 11.7 RANDOM PICTURES 424 11.7.1 THE SIERPINSKI TRIANGLE 424 11.7.2 TREES AND LEAVES 429 REFERENCES 441 COLOR APPENDIX 443
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spellingShingle	Andersson, Göran Applied mathematics with Maple Maple V 4.0 (DE-588)4407788-9 gnd
subject_GND	(DE-588)4407788-9
title	Applied mathematics with Maple
title_auth	Applied mathematics with Maple
title_exact_search	Applied mathematics with Maple
title_full	Applied mathematics with Maple Göran Andersson
title_fullStr	Applied mathematics with Maple Göran Andersson
title_full_unstemmed	Applied mathematics with Maple Göran Andersson
title_short	Applied mathematics with Maple
title_sort	applied mathematics with maple
topic	Maple V 4.0 (DE-588)4407788-9 gnd
topic_facet	Maple V 4.0
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008459918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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