Geometry of curves and surfaces with MAPLE:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 310 S. graph. Darst. |
| ISBN: | 0817640746 3764340746 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometry of curves and surfaces with MAPLE |c Vladimir Rovenski |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2000 | |
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Record in the Search Index
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| adam_text | Contents
Preface v
MAPLE V: A Quick Reference 1
I Functions and Graphs with MAPLE 5
1 Graphs of Tabular and Continuous Functions 7
1.1 Basic Two Dimensional Plots 7
1.2 Graphs of Functions Obtained from Elementary Functions 13
1.3 Graphs of Special Functions 15
1.4 Transformations of Graphs 17
1.5 Investigation of Functions Using Derivatives 19
2 Graphs of Composed Functions 21
2.1 Graphs of Piecewise Continuous Functions 21
2.2 Graphs of Piecewise Differentiable Functions 26
3 Interpolation of Functions 33
3.1 Polynomial Interpolation of Functions 33
3.2 Spline Interpolation of Functions 36
3.3 Constructing Curves Using Spline Functions 38
4 Approximation of Functions 41
4.1 Method of Least Squares 41
viii Contents
4.2 Bezier Curves 42
4.3 Rational Bezier Curves 43
II Curves with MAPLE 45
5 Plane Curves in Rectangular Coordinates 47
5.1 What Is a Curve? 48
5.2 Plotting Cycloidal Curves 49
5.3 Experiment with Polar Coordinates 52
5.4 Some Other Remarkable Curves 53
5.5 Level Curves, Vector Fields, and Trajectories 54
5.6 Level Curves of Functions and Extremal Problems . . 57
6 Curves in Polar Coordinates 61
6.1 Basic Plots in Polar Coordinates 61
6.2 Remarkable Curves in Polar Coordinates 66
6.3 Inversion of Curves 69
6.4 Spirals 71
6.5 Roses and Crosses 72
7 Asymptotes of Curves 75
8 Space Curves 79
8.1 Introduction 79
8.2 Knitting on Surfaces of Revolution 83
8.3 Plotting Curves (Tubes) with Shadow 87
8.4 Trajectories of Vector Fields in Space 93
9 Tangent Lines to a Curve 95
9.1 Tangent Lines 95
9.2 Envelope Curve of a Family of Curves 100
9.3 Mathematical Embroidery 102
9.4 Evolute and Evolvent (Involute): Caustic 105
9.5 Parallel Curves 108
10 Singular Points on Curves 111
10.1 Singular Points on Parametrized Curves 112
10.2 Singular Points on Implicitly Defined Plane Curves . . 113
10.3 Unusual Singular Points on Plane Curves 115
11 Length and Center of Mass of a Curve 117
Contents ix
11.1 Basic Facts 117
11.2 Calculation of Length and Center of Mass 119
12 Curvature and Torsion of Curves 125
12.1 Basic Facts 125
12.2 Curvature and Osculating Circle of a Curve in the Plane 127
12.3 Curvature and Torsion of a Curve in Space 129
12.4 Natural Equations of a Curve 131
13 Fractal Curves and Dimension 133
13.1 Sierpinski s Curves 133
13.2 Peano Curves 137
13.3 Koch Curves 140
13.4 Dragon Curve (or Polygon) 144
13.5 The Menger Curve 147
14 Spline Curves 151
14.1 Preliminary Facts and Examples 152
14.2 Composed Bezier Curves 154
14.3 Composed B Spline Curves 157
14.4 Beta Spline Curves 159
14.5 Interpolation Using Cubic Hermite Curves 167
14.6 Composed Catmull Rom Spline Curves 170
15 Non Euclidean Geometry in the Half Plane 173
15.1 Preliminary Facts 173
15.2 Examples of Visualization 175
16 Convex Hulls 189
III Polyhedra with MAPLE 191
17 Regular Polyhedra 193
17.1 What Is a Polyhedron? 194
17.2 Platonic Solids 198
17.3 Star Shaped Polyhedra 204
18 Semi Regular Polyhedra 211
18.1 What Are Semi Regular Polyhedra? 212
18.2 Programs for Plotting Semi Regular Polyhedra .... 216
x Contents
IV Surfaces with MAPLE 229
19 Surfaces in Space 231
19.1 What Is a Surface? 231
19.2 Regular Parametrized Surface 235
19.3 Methods of Generating Surfaces 238
19.4 Tangent Planes and Normal Vectors 243
19.5 The Osculating Paraboloid and a Type of Smooth Point 252
19.6 Singular Points on Surfaces 259
20 Some Classes of Surfaces 265
20.1 Algebraic Surfaces 265
20.2 Surfaces of Revolution 268
20.3 Ruled Surfaces 275
20.4 Envelope of a One Parameter Family of Surfaces . . . 284
21 Some Other Classes of Surfaces 291
21.1 Canal Surfaces and Tubes 291
21.2 Translation Surfaces 293
21.3 Twisted Surfaces 294
21.4 Parallel Surfaces (Equidistants) 295
21.5 Pedal and Podoid Surfaces 296
21.6 Cissoidal and Conchoidal Maps 298
21.7 Inversion of a Surface 299
References 303
Index 307
|
| any_adam_object | 1 |
| author | Rovenski, Vladimir 1953- |
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| author_facet | Rovenski, Vladimir 1953- |
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| author_sort | Rovenski, Vladimir 1953- |
| author_variant | v r vr |
| building | Verbundindex |
| bvnumber | BV013227596 |
| classification_rvk | SK 370 ST 601 |
| ctrlnum | (OCoLC)247289653 (DE-599)BVBBV013227596 |
| discipline | Informatik Mathematik |
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| id | DE-604.BV013227596 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:05Z |
| institution | BVB |
| isbn | 0817640746 3764340746 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009014664 |
| oclc_num | 247289653 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-739 DE-92 DE-634 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-739 DE-92 DE-634 |
| physical | X, 310 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Rovenski, Vladimir 1953- Verfasser (DE-588)12012985X aut Geometry of curves and surfaces with MAPLE Vladimir Rovenski Boston [u.a.] Birkhäuser 2000 X, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Maple V (DE-588)4276266-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009014664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rovenski, Vladimir 1953- Geometry of curves and surfaces with MAPLE Differentialgeometrie (DE-588)4012248-7 gnd Maple V (DE-588)4276266-2 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4276266-2 |
| title | Geometry of curves and surfaces with MAPLE |
| title_auth | Geometry of curves and surfaces with MAPLE |
| title_exact_search | Geometry of curves and surfaces with MAPLE |
| title_full | Geometry of curves and surfaces with MAPLE Vladimir Rovenski |
| title_fullStr | Geometry of curves and surfaces with MAPLE Vladimir Rovenski |
| title_full_unstemmed | Geometry of curves and surfaces with MAPLE Vladimir Rovenski |
| title_short | Geometry of curves and surfaces with MAPLE |
| title_sort | geometry of curves and surfaces with maple |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Maple V (DE-588)4276266-2 gnd |
| topic_facet | Differentialgeometrie Maple V |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009014664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rovenskivladimir geometryofcurvesandsurfaceswithmaple |