Mathematica by example:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier Acad. Press
2004
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 571 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0120415631 |
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MARC
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| 245 | 1 | 0 | |a Mathematica by example |c Martha L. Abell and James P. Braselton |
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| _version_ | 1804138991721644032 |
|---|---|
| adam_text | Titel: Mathematica by example
Autor: Abell, Martha L
Jahr: 2004
Contents
Preface ix
1 Getting Started 1
1.1 Introduction to Mathematica ............................................1
A Note Regarding Different Versions of Mathematica................3
1.1.1 Getting Started with Mathematica..............................3
Preview......................................................................9
1.2 Loading Packages..........................................................10
A Word of Caution........................................................13
1.3 Getting Help from Mathematica..........................................14
Mathematica Help ........................................................18
The Mathematica Menu..................................................22
2 Basic Operations on Numbers, Expressions, and Functions 23
2.1 Numerical Calculations and Built-in Functions........................23
2.1.1 Numerical Calculations..........................................23
2.1.2 Built-in Constants........................ 26
2.1.3 Built-in Functions................................................27
A Word of Caution........................................................30
2.2 Expressions and Functions: Elementary Algebra......................31
2.2.1 Basic Algebraic Operations on Expressions....................31
2.2.2 Naming and Evaluating Expressions..........................37
Two Words of Caution............................................38
2.2.3 Defining and Evaluating Functions............................39
2.3 Graphing Functions, Expressions, and Equations......................45
Contents
2.3.1 Functions of a Single Variable ..................................45
2.3.2 Parametric and Polar Plots in Two Dimensions ..............58
2.3.3 Three-Dimensional and Contour Plots; Graphing Equations 65
2.3.4 Parametric Curves and Surfaces in Space......................75
2.4 Solving Equations.............................
2.4.1 Exact Solutions of Equations....................................SI
2.4.2 Approximate Solutions of Equations ..........................90
Calculus 97
3.1 Limits........................................................................97
3.1.1 Using Graphs and Tables to Predict Limits....................98
3.1.2 Computing Limits................................................99
3.1.3 One-Sided Limits..................................................102
3.2 Differential Calculus......................................................104
3.2.1 Definition of the Derivative......................................104
3.2.2 Calculating Derivatives..........................................107
3.2.3 Implicit Differentiation..........................................110
3.2.4 Tangent Lines......................................................Ill
3.2.5 The First Derivative Test and Second Derivative Test .... 123
3.2.6 Applied Max/Min Problems....................................128
3.2.7 Antidifferentiation................................................138
3.3 Integral Calculus..........................................................141
3.3.1 Area................................................................141
3.3.2 The Definite Integral..............................................147
3.3.3 Approximating Definite Integrals..............................153
3.3.4 Area................................................................156
3.3.5 Arc Length........................................................162
3.3.6 Solids of Revolution..............................................167
3.4 Series........................................................................173
3.4.1 Introduction to Sequences and Series..........................173
3.4.2 Convergence Tests................................................178
3.4.3 Alternating Series................................................182
3.4.4 Power Series......................................................184
3.4.5 Taylor and Maclaurin Series ....................................187
3.4.6 Taylor s Theorem..................................................192
3.4.7 Other Series........................................................196
3.5 Multi-Variable Calculus ..................................................198
3.5.1 Limits of Functions of Two Variables............. 198
3.5.2 Partial and Directional Derivatives .............. 201
3.5.3 Iterated Integrals......................... 218
Contents v/i
4 Introduction to Lists and Tables 229
4.1 Lists and List Operations..................................................229
4.1.1 Defining Lists......................................................229
4.1.2 Plotting Lists of Points............................................233
4.2 Manipulating Lists: More on Part and Map............................248
4.2.1 More on Graphing Lists; Graphing Lists of Points Using
Graphics Primitives..............................................258
4.2.2 Miscellaneous List Operations..................................267
4.3 Mathematics of Finance ..................................................267
4.3.1 Compound Interest..............................................268
4.3.2 Future Value......................................................270
4.3.3 Annuity Due......................................................271
4.3.4 Present Value......................................................273
4.3.5 Deferred Annuities................................................274
4.3.6 Amortization......................................................275
4.3.7 More on Financial Planning . ...................................280
4.4 Other Applications........................................................287
4.4.1 Approximating Lists with Functions ..........................287
4.4.2 Introduction to Fourier Series ..................................294
4.4.3 The Mandelbrot Set and Julia Sets..............................308
5 Matrices and Vectors 327
5.1 Nested Lists: Introduction to Matrices, Vectors, and
Matrix Operations..........................................................327
5.1.1 Defining Nested Lists, Matrices, and Vectors..................327
5.1.2 Extracting Elements of Matrices................................334
5.1.3 Basic Computations with Matrices..............................337
5.1.4 Basic Computations with Vectors ..............................342
5.2 Linear Systems of Equations..............................................349
5.2.1 Calculating Solutions of Linear Systems
of Equations ......................................................349
5.2.2 Gauss-Jordan Elimination ......................................355
5.3 Selected Topics from Linear Algebra....................................362
5.3.1 Fundamental Subspaces Associated with Matrices..........362
5.3.2 The Gram-Schmidt Process . ................................364
5.3.3 Linear Transformations..........................................370
5.3.4 Eigenvalues and Eigenvectors..................................373
5.3.5 Jordan Canonical Form..........................................377
5.3.6 The QR Method ..................................................381
5.4 Maxima and Minima Using Linear Programming ....................384
viii
Contents
5.4.1 The Standard Form of a Linear Programming
Problem............................................................3^
5.4.2 The Dual Problem................................................386
5.5 Selected Topics from Vector Calculus....................................393
5.5.1 Vector-Valued Functions ........................................393
5.5.2 Line Integrals......................................................402
5.5.3 Surface Integrals..................................................407
5.5.4 A Note on Nonorientability......................................414
6 Differential Equations 429
6.1 First-Order Differential Equations ......................................429
6.1.1 Separable Equations..............................................429
6.1.2 Linear Equations..................................................434
6.1.3 Nonlinear Equations..............................................444
6.1.4 Numerical Methods..............................................448
6.2 Second-Order Linear Equations..........................................454
6.2.1 Basic Theory......................................................454
6.2.2 Constant Coefficients............................................455
6.2.3 Undetermined Coefficients......................................462
6.2.4 Variation of Parameters..........................................467
6.3 Higher-Order Linear Equations..........................................470
6.3.1 Basic Theory......................................................470
6.3.2 Constant Coefficients............................................470
6.3.3 Undetermined Coefficients......................................473
6.3.4 Laplace Transform Methods....................................485
6.3.5 Nonlinear Higher-Order Equations............................498
6.4 Systems of Equations......................................................498
6.4.1 Linear Systems....................................................498
6.4.2 Nonhomogeneous Linear Systems..............................515
6.4.3 Nonlinear Systems................................................519
6.5 Some Partial Differential Equations......................................538
6.5.1 The One-Dimensional Wave Equation..........................538
6.5.2 The Two-Dimensional Wave Equation..........................544
6.5.3 Other Partial Differential Equations............................556
|
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| author | Abell, Martha L. 1962- |
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| dewey-full | 510.285536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.285536 |
| dewey-search | 510.285536 |
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| discipline | Informatik Mathematik |
| edition | 3. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:36:59Z |
| institution | BVB |
| isbn | 0120415631 |
| language | English |
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| physical | XII, 571 S. graph. Darst. 1 CD-ROM (12 cm) |
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| publishDateSort | 2004 |
| publisher | Elsevier Acad. Press |
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| spelling | Abell, Martha L. 1962- Verfasser (DE-588)130087025 aut Mathematica by example Martha L. Abell and James P. Braselton 3. ed. Amsterdam [u.a.] Elsevier Acad. Press 2004 XII, 571 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematik (DE-588)4037944-9 s Mathematica Programm (DE-588)4268208-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017437992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abell, Martha L. 1962- Mathematica by example Mathematik (DE-588)4037944-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4268208-3 |
| title | Mathematica by example |
| title_auth | Mathematica by example |
| title_exact_search | Mathematica by example |
| title_full | Mathematica by example Martha L. Abell and James P. Braselton |
| title_fullStr | Mathematica by example Martha L. Abell and James P. Braselton |
| title_full_unstemmed | Mathematica by example Martha L. Abell and James P. Braselton |
| title_short | Mathematica by example |
| title_sort | mathematica by example |
| topic | Mathematik (DE-588)4037944-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | Mathematik Mathematica Programm |
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