Computer algebra recipes: a gourmet's guide to the mathematical models of science
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Undergraduate texts in contemporary physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0387951482 |
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| 245 | 1 | 0 | |a Computer algebra recipes |b a gourmet's guide to the mathematical models of science |c Richard H. Enns ; George C. McGuire |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XIV, 778 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in contemporary physics | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Mathematical models | |
| 650 | 4 | |a Physics |x Computer-assisted instruction | |
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| 650 | 0 | 7 | |a Computeralgebra |0 (DE-588)4010449-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1807954062983823360 |
|---|---|
| adam_text |
COMPUTE
R
ALGEBRA
RECIPES
A GOURMET'S GUIDE T
O
THE MGTTEMATFCAL
MODELS OF SCIENCE
RICHARD H. ENNS
GEORGE C. MCGUIRE
WITH 241 ILLUSTRATIONS
INCLUDES CD-ROM
SPRINGER
CONTENTS
PREFACE VII
INTRODUCTION 1
A. COMPUTE
R ALGEBR
A SYSTEM
S 1
B
. TH
E SPIRAL STAIRCAS
E T
O LEARNIN
G 3
C. HOW T
O CLIMB TH
E SPIRAL STAIRCAS
E 7
I THE APPETIZERS 9
1 TH
E PICTURE
S O
F SCIENC
E 1
1
1.1 INTRODUCTIO
N 11
1.2 DAT
A AN
D FUNCTIO
N PLOT
S 13
1.2.1 CORRECTIN
G FOR INFLATION 13
1.2.2 TH
E PLUMMETIN
G BADMINTO
N BIR
D 20
1.2.3 MINIMIZING TH
E TRAVEL TIM
E 29
1.3 LOG-LOG (POWER LAW) PLOT
S 33
1.3.1 CHIMPANZE
E BRAI
N SIZE 33
1.3.2 SCALING ARGUMENT
S AN
D GULLIVER'
S TRAVELS 38
1.4 CONTOU
R AN
D GRADIEN
T PLOT
S 43
1.4.1 TH
E SECRET MESSAGE 43
1.4.2 DESIGNING A SKI HILL 47
1.5 ANIMATE
D PLOT
S 53
1.5.1 WAVES AR
E DYNAMI
C 53
1.5.2 TH
E SAND
S OF TIM
E 56
2 DERIVIN
G MODE
L EQUATION
S
'
5
9
2.1 INTRODUCTIO
N 59
2.2 LINEAR CORRELATIO
N 60
2.2.1 WHA
T IS LINEAR CORRELATION
? 60
2.2.2 TH
E COR
N PALAC
E 61
2.3 LEAST SQUARE
S DERIVATION
S 63
2.3.1 REGRESSION ANALYSIS 63
2.3.2 WILL YOU BE BETTE
R OFF THA
N YOUR PARENTS
? 65
2.3.3 WHA
T WAS TH
E HEAR
T RAT
E OF A BRACHIOSAURUS
? 71
2.3.4 SENAT
E RENEWAL 78
CONTENTS
2.3.5 BIKINI SALES AND TH
E LOGISTIC CURVE 81
2.3.6 FOLLOWING THE DOW JONES INDEX 86
2.3.7 VARIATION OF
"G"
WITH LATITUD
E 93
2.3.8 FINDING ROMEO A JULIET 97
2.4 MULTIPLE REGRESSION EQUATIONS 101
2.4.1 REAL ESTAT
E APPRAISALS 102
2.4.2 AND THE WINNER IS? 107
ALGEBRAI
C MODEL
S 113
3.1 INTRODUCTION 113
3.2 ALGEBRAIC EXAMPLES 114
3.2.1 BOMBS VERSUS SCHOOLS 114
3.2.2 KIRCHHOFF RULES THE ELECTRICAL WORLD 121
3.2.3 THE WINDOW WASHER'S SECRET 128
3.2.4 THE SCIENCE STUDENT'
S SUMMER JOB INTERVIEW 134
3.2.5 ENVELOPE OF SAFETY 140
3.2.6 RAINBOW COUNTY 144
3.3 INTEGRAL EXAMPLES 150
3.3.1 THE GREAT PYRAMID OF CHEOPS 150
3.3.2 NOAH'S ARK 156
3.4 VECTOR EXAMPLES 166
3.4.1 VECTORIA'S MATHEMATICAL HERITAGE 166
3.4.2 AIN'T SHE SWEET 173
3.4.3 BORN CURL FREE 181
3.4.4 OF FLUX AND CIRCULATION AND COORDINATES TOO 186
MONT
E CARL
O METHOD
S 195
4.1 INTRODUCTION 195
4.2 RANDOM WALKS 197
4.2.1 TH
E CONCEPT 197
4.2.2 THE SOCCER FAN'S DRUNKEN WALK 200
4.2.3 BLOWIN' IN TH
E WIND 205
4.2.4 FLIGHT OF PENELOPE JITTE
R BUG 209
4.2.5 THA
T MEANDERING PERFUME MOLECULE 212
4.3 MONTE CARLO INTEGRATION 215
4.3.1 STANDARD NUMERICAL INTEGRATION ALGORITHMS 215
4.3.2 MONTE CARLO INTEGRATION "' .
.
219
4.3.3 WAIT AND BUY LATER! 220
4.3.4 WAIT AND BUY LATER! TH
E SEQUEL 224
4.3.5 ESTIMATING
N
229
4.3.6 CHARIOT OF FIRE AND DESTRUCTION 231
4.4 PROBABILITY DISTRIBUTIONS 236
4.4.1 OF NUTS AND BOLTS AND HOSPITAL BEDS TOO 236
4.4.2 THE ICE WINES OF RAINBOW COUNTY 243
4.5 MONTE CARLO STATISTICAL DISTRIBUTIONS 250
4.5.1 ESTIMATING
E
250
4.5.2 VAPOR DEPOSITION 255
CONTENTS
XI
II THE ENTREES 261
5 PHASE-PLAN
E PORTRAIT
S 263
5.1 INTRODUCTION 263
5.2 PHASE-PLANE PORTRAITS 263
5.2.1 STATIONARY OR SINGULAR POINTS 265
5.3 LINEAR ODE MODELS 268
5.3.1- TENURE POLICY AT EREHWON UNIVERSITY 268
5.3.2 VECTORIA INVESTIGATES THE RLC CIRCUIT 273
5.4 NONLINEAR ODE MODELS 280
5.4.1 CLASSIFICATION OF STATIONARY POINTS 280
5.4.2 RABBITS AND FOXES 284
5.4.3 THE MONA LISA OF NONLINEAR SCIENCE 292
5.4.4 MIKE CREATES A HIGHER-ORDER SINGULAR POINT 301
5.4.5 THE GNUS AND SUNG OF EREHWON 308
5.5 NONAUTONOMOUS ODES 314
5.5.1 CAN AN UNSTABLE SPRING FIND STABILITY? 314
5.5.2 THE PERIOD DOUBLING ROUTE TO CHAOS 317
6 LINEAR ODE MODEL
S 325
6.1 INTRODUCTION 325
6.2 SOLVING LINEAR ODES WITH MAPLE 326
6.3 FIRST-ORDER ODE MODELS 332
6.3.1 THERE GOES LOUIE'S ALIBI 332
6.3.2 THE WATER SKIER 341
6.4 SECOND-ORDER ODE MODELS 345
6.4.1 SHRINKING THE SAFETY ENVELOPE 345
6.4.2 HALLEY'S COMET 350
6.4.3 FRANK N. STEIN IS NOT HEARTLESS 358
6.4.4 VECTORIA FEELS THE FORCE AND HITS THE BOTTLE 362
6.5 BESSEL AND LEGENDRE ODE MODELS 369
6.5.1 INTRODUCTION TO SPECIAL FUNCTIONS 369
6.5.2 THE VIBRATING BUNGEE CORD 376
6.5.3 WHEEL OF MISFORTUNE 382
6.5.4 THE WEEDEATER 391
7 NONLINEAR ODE MODEL
S 397
7.1 INTRODUCTION _ 397
7.2 FIRST-ORDER MODELS 398
7.2.1 THE NONLINEAR DIODE 398
7.2.2 THE BAD BIRD EQUATION 402
7.2.3 THE STRUGGLE FOR EXISTENCE 407
7.3 SECOND-ORDER MODELS 414
7.3.1 PIRATES OF THE CARIBBEAN 414
7.3.2 OH WHAT SOUNDS WE HEAR! 418
7.3.3 THOSE LENNARD-JONES VIBRATIONAL BLUES 424
7.3.4 GOLF IS SUCH AN "UPLIFTING" EXPERIENCE 432
7.3.5 THIS WOULD BE A GREAT AMUSEMENT PARK RIDE 438
XII
CONTENTS
7.4 LIMIT CYCLES 445
7.4.1 TH
E BIZARR
E WORLD OF TH
E TUNNE
L DIODE OSCILLATOR .
. 445
7.4.2 FOLLOW THA
T RABBI
T 452
8 DIFFERENC
E EQUATIO
N MODEL
S 45
9
8.1 INTRODUCTIO
N 459
8.2 LINEAR DIFFERENCE EQUATIO
N MODELS 460
8.3 FIRST-ORDE
R LINEAR MODELS 461
8.3.1 THOS
E DRATTE
D GNAT
S 461
8.3.2 GONE FISHIN
G 464
8.4 SECOND-ORDER LINEA
R MODELS 467
8.4.1 FIBONACCI'
S ADA
M AN
D EVE RABBI
T 467
8.4.2 HOW RED IS YOUR BLOOD
? 471
8.4.3 FERMI-PASTA-ULA
M IS NOT A SPAGHETT
I WESTER
N 473
8.5 NONLINEAR DIFFERENCE EQUATIO
N MODELS 484
8.6 FIRST-ORDE
R NONLINEA
R MODELS 484
8.6.1 COMPETITIO
N FOR AVAILABLE RESOURCES 484
8.6.2 TH
E LOGISTIC MA
P AN
D COBWEB DIAGRAM
S 492
8.7 SECOND-ORDER NONLINEAR MODELS 499
8.7.1 TH
E BOUNCING BALL AR
T GALLERY 499
8.7.2 ONSE
T OF CHAOS
: A MODEL FOR TH
E OUTBREA
K OF WAR .
. 503
8.8 NUMERICALL
Y SOLVING ODE
S 513
8.8.1 FINIT
E DIFFERENCE APPROXIMATION
S T
O DERIVATIVES 513
8.8.2 RABBIT
S AN
D FOXES: TH
E SEQUEL 516
8.8.3 GLYCOLYTIC OSCILLATOR 521
9 SOM
E ANALYTI
C APPROACHE
S 52
7
9.1 INTRODUCTIO
N 527
9.2 CHECKING SOLUTIONS 527
9.2.1 TH
E PALAC
E OF TH
E GOVERNORS 527
9.2.2 PLA
Y IT
, SAM 532
9.2.3 TH
E THREE-PIEC
E STRIN
G 536
9.3 CALCULUS OF VARIATION
S 541
9.3.1 DRESS DESIGN, TH
E EREHWONESE WAY 541
9.3.2 QUEEN DIDO'
S PROBLE
M 548
9.3.3 TH
E HUMA
N FL
Y PLAN
S HIS ESCAP
E ROUT
E 552
9.4 FOURIER SERIES 559
9.4.1 HI C IS NOT ALWAYS A DRIN
K .
' 562
9.4.2 PLA
Y IT
, SAM: A NEW PERSPECTIV
E 565
9.4.3 VECTORIA SUMS A SERIES 569
1
0 FRACTA
L PATTERN
S 57
3
10.1 INTRODUCTIO
N 573
10.2 DIFFERENCE EQUATIO
N PATTERN
S 574
10.2.1 WALLPAPE
R FOR TH
E MIN
D 574
10.2.2 SIERPINSKI'S FRACTA
L GASKET 576
10.2.3 BARNSLEY'
S FERN 583
10.2.4 DOUADY'
S RABBI
T AN
D OTHE
R FAUN
A AN
D FLOR
A 588
CONTENTS
XIII
10.2.5 TH
E RINGS OF SATUR
N 592
10.3 ODE PATTERN
S 601
10.3.1 TH
E BUTTERFLY ATTRACTO
R 601
10.3.2 ROSSLER'S STRANGE ATTRACTO
R 606
10.4 CELLULAR AUTOMAT
A PATTERN
S 608
10.4.1 A NAVAHO RUG DESIGN 608
10.4.2 TH
E ONE OUT OF EIGHT RULE 611
II
I TH
E DESSERT
S 615
11 DIAGNOSTI
C TOOL
S FOR NONLINEA
R DYNAMIC
S 61
7
11.1 INTRODUCTION 617
11.2 THE POINCARE SECTION 617
11.2.1 THE CONCEPT 617
11.2.2 A RATTLE
R SIGNALS CHAOS 618
11.3 THE POWER SPECTRUM 622
11.3.1 THE CONCEPT 622
11.3.2 THE RATTLE
R RETURNS 624
11.4 THE BIFURCATION DIAGRAM 628
11.4.1 TH
E CONCEPT 628
11.4.2 PITCHFORKS AND OTHER BIFURCATIONS 629
11.5 THE LYAPUNOV EXPONENT 632
11.5.1 THE CONCEPT 632
11.5.2 MR. LYAPUNOV AGREES 633
11.6 RECONSTRUCTING AN ATTRACTO
R 635
11.6.1 THE CONCEPT 635
11.6.2 CHAOS VERSUS NOISE 636
12 LINEAR PD
E MODEL
S 64
1
12.1 INTRODUCTION 641
12.1.1 THE LINEAR PDES OF MATHEMATICAL PHYSICS 641
12.1.2 SEPARATION OF VARIABLES 643
12.2 DIFFUSION AND LAPLACE'S EQUATION MODELS 647
12.2.1 FREEING EXCALIBUR 647
12.2.2 AUSSIE BARBECUE 651
12.2.3 EREHWON INSTITUT
E OF TECHNOLOGY 655
12.2.4 HUGO AND TH
E ATOMIC BOMB 659
12.2.5 HUGO PREPARES FOR HIS JOB INTERVIEW 666
12.3 WAVE EQUATION MODELS 672
12.3.1 VECTORIA ENCOUNTERS SIMON LEGREE 672
12.3.2 HOMER'S JIGGLE TEST 676
12.3.3 VECTORIA'S SECOND PROBLEM 681
12.4 SEMI-INFINITE AND INFINITE DOMAINS 685
12.4.1 VECTORIA'S THIRD PROBLEM 686
12.4.2 ASSIGNMENT COMPLETE! 688
12.4.3 RADIOACTIVE CONTAMINATION 691
12.4.4 "PLAY IT
, SAM" REVISITED 696
XIV
CONTENTS
13 NONLINEAR PD
E MODELS
: SOLITO
N SOLUTIONS 701
13.1 INTRODUCTION 701
13.2 SOLITARY WAVES 702
13.3 THE GRAPHICAL HUNT FOR SOLITONS 704
13.3.1 OF KINKS AND ANTIKINKS 704
13.3.2 IN SEARCH OF BRIGHT SOLITONS 708
13.3.3 CAN THREE SOLITARY WAVES LIVE TOGETHER? 712
13.4 ANALYTIC SOLITON SOLUTIONS 715
13.4.1 FOLLOW THA
T WAVE! 715
13.4.2 LOOKING FOR A KINKY SOLUTION 719
14 SIMULATING PD
E MODEL
S 723
14.1 INTRODUCTION 723
14.2 DIFFUSION AND WAVE EQUATION MODELS 724
14.2.1 FREEING EXCALIBUR THE NUMERICAL WAY 724
14.2.2 VECTORIA SECRET 728
14.2.3 ENJOY THE KLEIN-GORDON VIBES 730
14.3 SOLITON COLLISIONS 734
14.3.1 TO BE OR NOT TO BE A SOLITON 734
14.3.2 ARE DIAMONDS A KINK'S BEST FRIEND? 738
EPILOGUE 745
BIBLIOGRAPH
Y 747
INDE
X 753 |
| any_adam_object | 1 |
| author | Enns, Richard H. 1938- McGuire, George 1940- |
| author_GND | (DE-588)115420894 (DE-588)115421890 |
| author_facet | Enns, Richard H. 1938- McGuire, George 1940- |
| author_role | aut aut |
| author_sort | Enns, Richard H. 1938- |
| author_variant | r h e rh rhe g m gm |
| building | Verbundindex |
| bvnumber | BV013902393 |
| callnumber-first | Q - Science |
| callnumber-label | QC30 |
| callnumber-raw | QC30 |
| callnumber-search | QC30 |
| callnumber-sort | QC 230 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 ST 600 |
| classification_tum | DAT 001f MAT 001f |
| ctrlnum | (OCoLC)123123546 (DE-599)BVBBV013902393 |
| dewey-full | 530/.078/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530/.078/5 |
| dewey-search | 530/.078/5 |
| dewey-sort | 3530 278 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013902393 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:15:54Z |
| institution | BVB |
| isbn | 0387951482 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009514220 |
| oclc_num | 123123546 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-739 DE-860 DE-634 DE-83 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-739 DE-860 DE-634 DE-83 |
| physical | XIV, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in contemporary physics |
| spelling | Enns, Richard H. 1938- Verfasser (DE-588)115420894 aut Computer algebra recipes a gourmet's guide to the mathematical models of science Richard H. Enns ; George C. McGuire New York [u.a.] Springer 2001 XIV, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in contemporary physics Mathematisches Modell Mathematical models Physics Computer-assisted instruction Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Computeralgebra (DE-588)4010449-7 s DE-604 Mathematisches Modell (DE-588)4114528-8 s McGuire, George 1940- Verfasser (DE-588)115421890 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Enns, Richard H. 1938- McGuire, George 1940- Computer algebra recipes a gourmet's guide to the mathematical models of science Mathematisches Modell Mathematical models Physics Computer-assisted instruction Mathematische Physik (DE-588)4037952-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4114528-8 (DE-588)4010449-7 |
| title | Computer algebra recipes a gourmet's guide to the mathematical models of science |
| title_auth | Computer algebra recipes a gourmet's guide to the mathematical models of science |
| title_exact_search | Computer algebra recipes a gourmet's guide to the mathematical models of science |
| title_full | Computer algebra recipes a gourmet's guide to the mathematical models of science Richard H. Enns ; George C. McGuire |
| title_fullStr | Computer algebra recipes a gourmet's guide to the mathematical models of science Richard H. Enns ; George C. McGuire |
| title_full_unstemmed | Computer algebra recipes a gourmet's guide to the mathematical models of science Richard H. Enns ; George C. McGuire |
| title_short | Computer algebra recipes |
| title_sort | computer algebra recipes a gourmet s guide to the mathematical models of science |
| title_sub | a gourmet's guide to the mathematical models of science |
| topic | Mathematisches Modell Mathematical models Physics Computer-assisted instruction Mathematische Physik (DE-588)4037952-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Mathematisches Modell Mathematical models Physics Computer-assisted instruction Mathematische Physik Computeralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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