Introduction to Maple:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2003
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 747 - 760 |
| Physical Description: | XVI, 828 S. graph. Darst. |
| ISBN: | 0387002308 9780387002309 |
Staff View
MARC
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| 100 | 1 | |a Heck, André |e Verfasser |0 (DE-588)1317603826 |4 aut | |
| 245 | 1 | 0 | |a Introduction to Maple |c André Heck |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2003 | |
| 300 | |a XVI, 828 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Literaturverz. S. 747 - 760 | ||
| 650 | 7 | |a Linguagem de programação |2 larpcal | |
| 650 | 7 | |a Maple (computerprogramma) |2 gtt | |
| 650 | 7 | |a Álgebra |2 larpcal | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Algebra |x Data processing | |
| 650 | 4 | |a Maple (Computer file) | |
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Record in the Search Index
| _version_ | 1804129891842523136 |
|---|---|
| adam_text | Contents
Preface
to the Third Edition
v
List of Tables
xv
1
Introduction to Computer Algebra
1
1.1
What is Computer Algebra?
................ 1
1.2
Computer Algebra Systems
................. 2
1.3
Some Properties of Computer Algebra Systems
..... 5
1.4
Advantages of Computer Algebra
............. 11
1.5
Limitations of Computer Algebra
............. 23
1.6
Design of Maple
....................... 29
2
The First Steps: Calculus on Numbers
33
2.1
Getting Started
....................... 33
2.2
Getting Help
......................... 36
2.3
Integers and Rational Numbers
.............. 41
2.4
Irrational Numbers and
Floating-Point
Numbers
..... 46
2.5
Algebraic Numbers
..................... 53
2.6
Complex Numbers
...................... 58
2.7
Exercises
........................... 63
3
Variables and Names
65
3.1
Assignment and Unassignment
............... 65
3.2
Evaluation
.......................... 73
χ
Contents
3.3
Names of
Variables..................... 77
3.4
Basic Data Types
...................... 83
3.5
Attributes
.......................... 88
3.6
Properties
.......................... 89
3.7
Exercises
........................... 93
4
Getting Around with Maple
95
4.1
Maple Input and Output
.................. 95
4.2
The Maple Library
..................... 101
4.3
Reading and Writing Files
................. 106
4.4
Importing and Exporting Numerical Data
........ 113
4.5
Low-level I/O
........................ 116
4.6
Code Generation
...................... 127
4.7
Changing Maple to Your Own Taste
........... 133
4.8
Exercises
........................... 137
5
Polynomials and Rational Functions
139
5.1
Univariate Polynomials
................... 139
5.2
Multivariate Polynomials
.................. 145
5.3
Rational Functions
..................... 147
5.4
Conversions
......................... 148
5.5
Exercises
........................... 151
6
Internal Data Representation and Substitution
153
6.1
Internal Representation of Polynomials
.......... 153
6.2
Generalized Rational Expressions
............. 159
6.3
Substitution
......................... 161
6.4
Exercises
........................... 174
7
Manipulation of Polynomials and Rational Expressions
175
7.1
Expansion
.......................... 175
7.2
Factorization
......................... 178
7.3
Canonical Form and Normal Form
............. 181
7.4
Normalization
........................ 183
7.5
Collection
.......................... 185
7.6
Sorting
............................ 187
7.7
Exercises
........................... 188
8
Functions
189
8.1
Mathematical Functions
.................. 189
8.2
Arrow Operators
...................... 193
8.3
Piecewise Defined Functions
................ 195
8.4
Maple Procedures
...................... 201
8.5
Recursive Procedure Definitions
.............. 204
8.6
unapply
........................... 208
Contents xi
8.7
Operations on Functions
.................. 209
8.8
Anonymous Functions
................... 210
8.9
Exercises
........................... 211
9
Differentiation
213
9.1
Symbolic Differentiation
.................. 213
9.2
Automatic Differentiation
................. 220
9.3
Exercises
........................... 224
10
Integration and Summation
225
10.1
Indefinite Integration
.................... 225
10.2
Definite Integration
..................... 234
10.3
Numerical Integration
.................... 239
10.4
Integral Transforms
..................... 241
10.5
Assisting Maple s Integrator
................ 250
10.6
Summation
.......................... 255
10.7
Exercises
........................... 260
11
Series, Approximation, and Limits
265
11.1
Truncated Series
....................... 265
11.2
Approximation of Functions
................ 276
11.3
Power Series
......................... 281
11.4
Limits
............................ 285
11.5
Exercises
........................... 287
12
Composite Data Types
289
12.1
Sequence
........................... 289
12.2
Set
.............................. 292
12.3
List
.............................. 294
12.4
Arrays
............................ 300
12.5
Table: table
......................... 316
12.6
Last Name Evaluation
................... 319
12.7
Rectangular Table: rtable
................. 321
12.8
Record Data Structure
................... 325
12.9
Function Call
........................ 326
12.10
Conversion between Composite Data Types
....... 328
12.11
Exercises
........................... 331
13
The Assume Facility
333
13.1
The Need for an Assume Facility
............. 333
13.2
Basics of assume
...................... 338
13.3
An Algebra of Properties
.................. 342
13.4
Implementation of assume
................. 344
13.5
Exercises
........................... 350
13.6
Hierarchy of Properties
................... 350
xii Contents
14
Simplification
353
14.1 Automatic
Simplification
.................. 354
14.2
expand
........................... 356
14.3
combine
........................... 364
14.4
simplify
........................... 370
14.5
convert
........................... 375
14.6
Trigonometric Simplification
................ 379
14.7
Simplification w.r.t. Side Relations
............ 382
14.8
Control Over Simplification
................ 386
14.9
Defining Your Own Simplification Routines
........ 391
14.10
Exercises
........................... 397
14.11
Simplification Chart
..................... 399
15
Graphics
401
15.1
Some Basic Two-Dimensional Plots
............ 403
15.2
Options of plot
....................... 407
15.3
The Structure of Two-Dimensional Graphics
....... 418
15.4
The plottools Package
.................. 422
15.5
Special Two-Dimensional Plots
.............. 426
15.6
Two-Dimensional Geometry
................ 436
15.7
Plot Aliasing
......................... 438
15.8
A Common Mistake
..................... 439
15.9
Some Basic Three-Dimensional Plots
........... 441
15.10
Options of plot3d
...................... 442
15.11
The Structure of Three-Dimensional Graphics
...... 448
15.12
Special Three-Dimensional Plots
.............. 452
15.13
Data Plotting
........................ 459
15.14
Animation
.......................... 469
15.15
List of Plot Options
..................... 472
15.16
Exercises
........................... 477
16
Solving Equations
481
16.1
Equations in One Unknown
................ 481
16.2
Abbreviations in solve
................... 483
16.3
Some Difficulties
....................... 485
16.4
Systems of Equations
.................... 492
16.5
The
Gröbner
Basis Method
................. 501
16.6
Inequalities
.......................... 508
16.7
Numerical Solvers
...................... 510
16.8
Other Solvers in Maple
................... 512
16.9
Exercises
........................... 519
17
Differential Equations
521
17.1
First Glance at ODEs
.................... 522
17.2
Analytic Solutions
...................... 524
Contents xiii
17.3
Lie
Point
Symmetries for ODEs
.............. 538
17.4
Taylor Series Method
.................... 560
17.5
Power Series Method
.................... 561
17.6
Numerical Solutions
..................... 566
17.7
Graphical Methods
..................... 580
17.8
Change of Coordinates
................... 586
17.9
Perturbation Methods
................... 590
17.10
Partial Differential Equations
............... 600
17.11
Lie Point Symmetries of PDEs
............... 615
17.12
Exercises
........................... 617
18
The LinearAlgebra Package
619
18.1
Loading the LineaxAlgebra Package
........... 619
18.2
Creating Vectors and Matrices
............... 621
18.3
Vector and Matrix Arithmetic
............... 629
18.4
Basic Matrix Functions
................... 634
18.5
Structural Operations
.................... 641
18.6
Vector Operations
...................... 645
18.7
Standard Forms of Matrices
................ 646
18.8
Numeric Linear Algebra
.................. 656
18.9
Exercises
........................... 660
19
Linear Algebra: Applications
663
19.1
Kinematics of the Stanford Manipulator
......... 663
19.2
A S-Compartment Model of Cadmium Transfer
..... 669
19.3
Molecular-Orbital Hiickel Theory
............. 680
19.4
Vector Calculus
....................... 687
19.5
Moore-Penrose Inverse
................... 693
19.6
Exercises
........................... 694
20
A Bird s-Eye View of
Gröbner
Bases
697
20.1
Introduction
......................... 697
20.2
Elementary Solution Methods
............... 702
20.2.1
Heuristic Method
.................. 702
20.2.2
Gaussian Elimination-Like Method
........ 702
20.2.3
Conclusion
...................... 703
20.3
Basics of the
Gröbner
Basis Method
............ 703
20.3.1
Term Ordering
................... 704
20.3.2
Polynomial Reduction and Normal Form
..... 710
20.3.3
Characterization of
a
Gröbner
Basis
........ 712
20.3.4
The Buchberger Algorithm
............. 714
20.3.5
Improvements of Buchberger s Algorithm
..... 716
20.4
Properties and Applications of
Gröbner
Bases
...... 719
20.4.1
Equivalence of Systems of Polynomial Equations
720
20.4.2
Dimension, Hilbert Series and Hubert Polynomial
721
xiv Contents
20.4.3
Solvability of Polynomial Equations
........ 725
20.4.4
Finite Solvability of Polynomial Equations
.... 729
20.4.5
Counting of Finite Solutions
............ 730
20.4.6
Converting a System of Polynomial Equations into
Triangular Form
................... 732
20.4.7
Finding a Univariate Polynomial
......... 734
20.4.8
Decomposition of Ideals
.............. 735
20.4.9
An Example From Robotics
............ 739
20.4.10Implicitization of Parametric Objects
....... 740
20.4.11
Invertibility of Polynomial Mappings
....... ,742
20.4.12
Simplification of Expressions
............ 742
20.4.13
Working over General Algebras
.......... 743
20.5
Exercises
........................... 745
References
747
Index
761
|
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| author_GND | (DE-588)1317603826 |
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 3. ed. |
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| indexdate | 2024-07-09T19:12:21Z |
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| isbn | 0387002308 9780387002309 |
| language | English |
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| spelling | Heck, André Verfasser (DE-588)1317603826 aut Introduction to Maple André Heck 3. ed. New York, NY [u.a.] Springer 2003 XVI, 828 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 747 - 760 Linguagem de programação larpcal Maple (computerprogramma) gtt Álgebra larpcal Datenverarbeitung Algebra Data processing Maple (Computer file) Computeralgebra (DE-588)4010449-7 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Maple V 4.0 (DE-588)4407788-9 gnd rswk-swf Maple Programm (DE-588)4209397-1 s DE-604 Computeralgebra (DE-588)4010449-7 s Maple V 4.0 (DE-588)4407788-9 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Heck, André Introduction to Maple Linguagem de programação larpcal Maple (computerprogramma) gtt Álgebra larpcal Datenverarbeitung Algebra Data processing Maple (Computer file) Computeralgebra (DE-588)4010449-7 gnd Maple Programm (DE-588)4209397-1 gnd Maple V 4.0 (DE-588)4407788-9 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4209397-1 (DE-588)4407788-9 |
| title | Introduction to Maple |
| title_auth | Introduction to Maple |
| title_exact_search | Introduction to Maple |
| title_full | Introduction to Maple André Heck |
| title_fullStr | Introduction to Maple André Heck |
| title_full_unstemmed | Introduction to Maple André Heck |
| title_short | Introduction to Maple |
| title_sort | introduction to maple |
| topic | Linguagem de programação larpcal Maple (computerprogramma) gtt Álgebra larpcal Datenverarbeitung Algebra Data processing Maple (Computer file) Computeralgebra (DE-588)4010449-7 gnd Maple Programm (DE-588)4209397-1 gnd Maple V 4.0 (DE-588)4407788-9 gnd |
| topic_facet | Linguagem de programação Maple (computerprogramma) Álgebra Datenverarbeitung Algebra Data processing Maple (Computer file) Computeralgebra Maple Programm Maple V 4.0 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT heckandre introductiontomaple |