Mathematica in action: problem solving through visualization and computation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2010
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Weitere Informationen Inhaltsverzeichnis |
| Beschreibung: | XI, 578 S. teilw. farb. Ill., graph. Darst. |
| ISBN: | 9780387753669 0387753664 |
Internformat
MARC
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| 100 | 1 | |a Wagon, Stan |d 1951- |e Verfasser |0 (DE-588)172440114 |4 aut | |
| 245 | 1 | 0 | |a Mathematica in action |b problem solving through visualization and computation |c Stan Wagon |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a XI, 578 S. |b teilw. farb. Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Mathematica |g Programm |0 (DE-588)4268208-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematica |g Programm |0 (DE-588)4268208-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://extras.springer.com |3 Weitere Informationen | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020480466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020480466 | ||
Datensatz im Suchindex
| _version_ | 1804143134575165440 |
|---|---|
| adam_text | Contents
Preface
ix
0
A Brief
Introduction
1
0.1
Notational Conventions
2
0.2
Typesetting
З
0.3
Basic
Mathematical Functions
5
0.4
Using Functions
7
0.5
Replacements
12
0.6
Lists
13
0.7
Getting Information
15
0.8
Algebraic Manipulations
17
0.9
Customizing
Mathematica
19
0.10
Comprehensive Data Sets in
Mathematica
19
1
Plotting
23
1.1
Plot
24
1.2
An Arcsin Curiosity
26
1.3
Adaptive Plotting
28
1.4
Plotting Tables and Tabling Plots
31
1.5
Dealing with Discontinuities
34
1.6
ListPlot
37
1.7
ParametricPlot
42
1.8
Difficult Plots
48
2
Prime Numbers
53
2.1
Basic Number Theory Functions
54
2.2
Where the Primes Are
60
2.3
The Prime Number Race
66
2.4
Euclid and Fibonacci
70
2.5
Strong
Pseudoprimes
73
3
Rolling Circles
77
3.1
Discovering the Cycloid
78
3.2
The Derivative of the Trochoid
82
3.3
Abe Lincoln s Somersaults
84
3.4
The Cycloid s Intimate Relationship with Gravity
90
3.5
Bicycles, Square Wheels, and Square-Hole Drills
98
4
Three-Dimensional Graphs
113
4.1
Using Two-Dimensional Tools
114
4.2
Plotting Surf aces
■ 119
4.3
Mixed Partial Derivatives Need Not Be Equal
130
4.4
Failure of the Only-Critical-Pomt-in-Town Test
134
4.5
Raising Contours to New Heights
137
4.6
A New View of Pascal s Triangle
139
5
Dynamic Manipulations
141
5.1
Basic Manipulations
142
5.2
Control Variations
144
5.3
Locators
148
5.4
Fine Control
151
5.5
Three Case Studies
157
6
The Cantor Set, Real and Complex
169
6.1
The Real Cantor Set
170
6.2
The Cantor Function
173
6.3
Complex Cantor Sets
175
7
The Quadratic Map
179
7.1
Iterating Functions
180
7.2
The Four Flavors of Real Numbers
187
7.3
Attracting and Repelling Cycles
192
7.4
Measuring Instability: The Lyapunov Exponent
199
7.5
Bifurcations
202
8
The Recursive Turtle
209
8.1
The Literate Turtle
210
8.2
Space-Filling Curves
215
8.3
A Surprising Application
223
8.4
Trees, Mathematical and Botanical
233
9
Parametric Plotting of Surfaces
235
9.1
Introduction to ParametricPlotSD
236
9.2
A Classic Torus Dissection
243
9.3
The Villarceau Circles
250
9.4
Beautiful Surfaces
254
9.5
A Fractal Tetrahedron
261
10 Penrose
Tiles
267
10.1
Nonperiodic Tilings
268
10.2 Penrose
Tilings
270
10.3 Penrose
Rhombs
274
11
Complex Dynamics: Julia Sets and the
Mandelbrot set (by Mark McClure)
277
11.1
Complex Dynamics
278
11.2
Julia Sets and Inverse Iteration
284
11.3
Escape Time Algorithms and the Mandelbrot Set
292
12
Solving Equations
301
12.1
Solve
302
12.2
Diophantine Equations
306
12.3
LinearSolve
310
12.4
NSolve
312
12.5
FindRoot
314
12.6
Finding All Roots in an Interval
315
12.7
FindRoots2D
318
12.8
Two Applications
322
13
Optimization
329
13.1
FindMinimum
330
13.2
Algebraic Optimization
333
13.3
Linear Programming and Its Cousins
334
13.4
Case Study: Interval Methods for a SIAM Challenge
346
13.5
Case Study: Shadowing Chaotic Maps
353
13.6
Case Study: Finding the Best Cubic
360
14
Differential Equations
363
14.1
Solving Differential Equations
364
14.2
Stylish Plots
367
14.3
Pitfalls of Numerical Computing
376
14.4
Basins of Attraction
382
14.5
Modeling
385
15
Computational Geometry
399
15.1
Basic Computational Geometry
400
15.2
The Art Gallery Theorem
404
15.3
A Very Strange Room
406
15.4
More Euclid
413
16
Check Digits and the Pentagon
423
16.1
The Group of the Pentagon
424
16.2
The Perfect Dihedral Method
427
17
Coloring Planar Maps
431
17.1
Introduction to Combinatorial
432
17.2
Planar Maps
437
17.3
Euler s Formula
441
17.4
Kempe s Attempt
445
17.5
Kempe
Resurrected
449
17.6
Map Coloring
458
17.7
A Great Circle Conjecture
468
18
New Directions for
π
473
18.1
The Classical Theory of
я
474
18.2
The Postmodern Theory of
π
480
18.3
A Most Depressing Proof
483
18.4
Variations on the Theme
488
19
The Banach-Tarski Paradox
491
19.1
A Paradoxical Free Product
492
19.2
A Hyperbolic Representation of the Group
495
19.3
The Geometrical Paradox
499
20
The Riemann
Zeta
Function
505
20.1
The Riemann
Zeta
Function
506
20.2
The Influence of the Zeros of
ζ
on the Distribution of Primes
512
20.3
A Backwards Look at Riemann s R(x)
519
21
Miscellany
523
21.1
An Educational Integral
524
21.2
Making the Alternating Harmonic Series Disappear
525
21.3
Bulletproof Prime Numbers
528
21.4
Gaussian Moats
530
21.5
Frobenius Number by Graphs
536
21.6
Benford s Law of First Digits
542
References
557
Mathematica
Index
566
Subject Index
572
|
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| author_GND | (DE-588)172440114 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.285/536 |
| dewey-search | 510/.285/536 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV036559077 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:42:50Z |
| institution | BVB |
| isbn | 9780387753669 0387753664 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020480466 |
| oclc_num | 699689613 |
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| physical | XI, 578 S. teilw. farb. Ill., graph. Darst. |
| publishDate | 2010 |
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| publisher | Springer |
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| spelling | Wagon, Stan 1951- Verfasser (DE-588)172440114 aut Mathematica in action problem solving through visualization and computation Stan Wagon 3. ed. New York, NY Springer 2010 XI, 578 S. teilw. farb. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 s DE-604 http://extras.springer.com Weitere Informationen Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020480466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wagon, Stan 1951- Mathematica in action problem solving through visualization and computation Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4268208-3 |
| title | Mathematica in action problem solving through visualization and computation |
| title_auth | Mathematica in action problem solving through visualization and computation |
| title_exact_search | Mathematica in action problem solving through visualization and computation |
| title_full | Mathematica in action problem solving through visualization and computation Stan Wagon |
| title_fullStr | Mathematica in action problem solving through visualization and computation Stan Wagon |
| title_full_unstemmed | Mathematica in action problem solving through visualization and computation Stan Wagon |
| title_short | Mathematica in action |
| title_sort | mathematica in action problem solving through visualization and computation |
| title_sub | problem solving through visualization and computation |
| topic | Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | Mathematica Programm |
| url | http://extras.springer.com http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020480466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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