Mathematica by example:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier Academic Press
2009
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 564 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780123743183 0123743184 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematica by example |c Martha L. Abell and James P. Braselton |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier Academic Press |c 2009 | |
| 300 | |a XI, 564 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 630 | 0 | 4 | |a Mathematica (Computer file) |
| 650 | 4 | |a Mathematica (Computer file) | |
| 650 | 4 | |a Mathematics / Data processing | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x Data processing | |
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Record in the Search Index
| _version_ | 1809768531324043264 |
|---|---|
| adam_text |
Contents
Preface
. ix
CHAPTER
1
Getting Started
ι
1.1
Introduction to
Mathematica
. 1
A Note Regarding Different Versions of
Mathematica
. 2
1.1.1
Getting Started with
Mathematica
. 3
Preview
. 13
Five Basic Rules of
Mathematica
Syntax
. 13
1.2
Loading Packages
. 13
1.2.1
Packages Included with Older Versions of
Mathematica
. 14
1.2.2
Loading New Packages
. 15
1.3
Getting Help from
Mathematica
. 17
Mathematica
Help
. 24
1.4
Exercises
. 28
CHAPTER
2
Basic Operations on Numbers,
Expressions, and Functions
31
2.1
Numerical Calculations and Built-in Functions
. 31
2.1.1
Numerical Calculations
. 31
2.1.2
Built-in Constants
. 34
2.1.3
Built-in Functions
. 35
A Word of Caution
. 38
2.2
Expressions and Functions: Elementary Algebra
. 39
2.2.1
Basic Algebraic Operations on Expressions
. 39
2.2.2
Naming and Evaluating Expressions
. 44
2.2.3
Defining and Evaluating Functions
. 41
2.3
Graphing Functions, Expressions, and Equations
. 52
2.3.1
Functions of a Single Variable
. 52
2.3.2
Parametric and Polar Plots in Two Dimensions
. 65
2.3.3
Three-Dimensional and Contour Plots:
Graphing Equations
. 71
2.3.4
Parametric Curves and Surfaces in Space
. 82
2.35
Miscellaneous Comments
. 94
2.4
Solving Equations
. 100
2.4.1
Exact Solutions of Equations
. 100
2.4.2
Approximate Solutions of Equations
. 110
2.5
Exercises
. 115
Contents
CHAPTER
3
Calculus H7
3.1
Limits and Continuity
. 117
3.1.1
Using Graphs and Tables to Predict Limits
. 117
312
Computing Limits
. 121
3.1-3
One-Sided limits
. 123
3-1.4
Continuity
. 124
3.2
Differential Calculus
. 128
3.2.1
Definition of the Derivative
. 128
3.2.2
Calculating Derivatives
. 135
32.3
Implicit Differentiation
. 138
3.2.4
Tangent lines
. 139
3.2.5
The First Derivative Test and Second
Derivative Test
. 148
32.6
Applied
Max/Min
Problems
. 156
32.7
Antidifferentiation
. 164
3.3
Integral Calculus
.
l68
3.3.1
Area
. 168
332
The Definite Integral
. 174
3.3.3
Approximating Definite Integrals
. 179
3.3.4
Area
. 180
335
Arc Length
. 186
33.6
Solids of Revolution
. 190
3.4
Series
. 201
3.4.1
Introduction to Sequences and Series
. 201
3-4.2
Convergence Tests
. 205
3-4.3
Alternating Series
. 209
З.4.4
Power Series
. 210
3-4.5
Taylor and Maclaurin Series
. 213
3-4.6
Taylor's Theorem
. 217
З.4.7
Other Series
. 220
3.5 Multivariable
Calculus
. 221
35.1
limits of Functions of Two Variables
. 222
35.2
Partial and Directional Derivatives
. 224
35.3
Iterated Integrals
. 238
3.6
Exercises
. 246
CHAPTER
4
Introduction to Lists and Tables
251
4-1
Lists and List Operations
. 251
41.1
Defining lists
. 251
4.1.2
Plotting lists of Points
. 258
4-2
Manipulating lists: More on Part and Map
. 269
4.2.1
More on Graphing lists: Graphing lists of Points
Using Graphics Primitives
. 277
4.2.2
Miscellaneous list Operations
. 283
Contents
I
vii
4.3
Other
Applications
. 283
4.3.1
Approximating lists with Functions
. 283
4.32
Introduction to Fourier Series
. 287
4.33
The Mandelbrot Set and Julia Sets
. 299
4.4
Exercises
. 311
CHAPTER
5
Matrices and Vectors: Topics from
Linear Algebra and Vector Calculus
317
5.1
Nested lists: Introduction to Matrices, Vectors, and
Matrix Operations
. 317
5.1.1
Defining Nested lists, Matrices, and Vectors
. 317
5.1.2
Extracting Elements of Matrices
. 322
5.1.3
Basic Computations with Matrices
. 325
5.1.4
Basic Computations with Vectors
. 329
5.2
Linear Systems of Equations
. 337
5.2.1
Calculating Solutions of linear Systems of
Equations
. 337
5.2.2
Gauss-Jordan Elimination
. 342
5.3
Selected Topics from linear Algebra
. 349
5.3.1
Fundamental Subspaces Associated with
Matrices
. 349
5.32
The Gram-Schmidt Process
. 351
5.33
linear Transformations
. 355
5.3-4
Eigenvalues and Eigenvectors
. 358
5.3.5
Jordan Canonical Form
. 361
5.36
The QR Method
. 364
5.4
Maxima and Minima Using linear Programming
. 366
5.4.1
The Standard Form of a linear Programming
Problem
. 366
5.4.2
The Dual Problem
. 368
5.5
Selected Topics from Vector Calculus
. 374
5.5.1
Vector-Valued Functions
. 374
5.5.2
line Integrals
. 384
5.5.3
Surface Integrals
. 387
5.5.4
A Note on Nonorientability
. 391
5.5-5
More on Tangents, Normals, and Curvature in
72 . 404
5.6
Matrices and Graphics
. 415
5.7
Exercises
. 430
CHAPTER
6
Applications Related to Ordinary and
Partial Differential Equations
435
6.1
First-Order Differential Equations
. 435
6.1.1
Separable Equations
. 435
6.1.2
linear Equations
. 442
vili
I Contents
6.1.3
Nonlinear Equations
. 450
6.1.4
Numerical Methods
. 453
6.2
Second-Order Linear Equations
. 457
6.2.1
Basic Theory
. 457
6.2.2
Constant Coefficients
. 458
6.2.3
Undetermined Coefficients
. 464
6.2.4
Variation of Parameters
. 470
6.3
Higher-Order Linear Equations
. 472
6.3.1
Basic Theory
. 472
6.3.2
Constant Coefficients
. 473
6.3.3
Undetermined Coefficients
. 475
6.3.4
Laplace Transform Methods
. 481
6.3.5
Nonlinear Higher-Order Equations
. 492
6.4
Systems of Equations
. 492
6.4.1
Linear Systems
. 492
6.4.2
Nonhomogeneous Linear Systems
. 505
6.4.3
Nonlinear Systems
. 511
6.5
Some Partial Differential Equations
. 532
6.5.1
The One-Dimensional Wave Equation
. 532
6.5.2
The Two-Dimensional Wave Equation
. 537
6.5.3
Other Partial Differential Equations
. 547
6.6
Exercises
. 550
References
557
Index
559 |
| adam_txt |
Contents
Preface
. ix
CHAPTER
1
Getting Started
ι
1.1
Introduction to
Mathematica
. 1
A Note Regarding Different Versions of
Mathematica
. 2
1.1.1
Getting Started with
Mathematica
. 3
Preview
. 13
Five Basic Rules of
Mathematica
Syntax
. 13
1.2
Loading Packages
. 13
1.2.1
Packages Included with Older Versions of
Mathematica
. 14
1.2.2
Loading New Packages
. 15
1.3
Getting Help from
Mathematica
. 17
Mathematica
Help
. 24
1.4
Exercises
. 28
CHAPTER
2
Basic Operations on Numbers,
Expressions, and Functions
31
2.1
Numerical Calculations and Built-in Functions
. 31
2.1.1
Numerical Calculations
. 31
2.1.2
Built-in Constants
. 34
2.1.3
Built-in Functions
. 35
A Word of Caution
. 38
2.2
Expressions and Functions: Elementary Algebra
. 39
2.2.1
Basic Algebraic Operations on Expressions
. 39
2.2.2
Naming and Evaluating Expressions
. 44
2.2.3
Defining and Evaluating Functions
. 41
2.3
Graphing Functions, Expressions, and Equations
. 52
2.3.1
Functions of a Single Variable
. 52
2.3.2
Parametric and Polar Plots in Two Dimensions
. 65
2.3.3
Three-Dimensional and Contour Plots:
Graphing Equations
. 71
2.3.4
Parametric Curves and Surfaces in Space
. 82
2.35
Miscellaneous Comments
. 94
2.4
Solving Equations
. 100
2.4.1
Exact Solutions of Equations
. 100
2.4.2
Approximate Solutions of Equations
. 110
2.5
Exercises
. 115
Contents
CHAPTER
3
Calculus H7
3.1
Limits and Continuity
. 117
3.1.1
Using Graphs and Tables to Predict Limits
. 117
312
Computing Limits
. 121
3.1-3
One-Sided limits
. 123
3-1.4
Continuity
. 124
3.2
Differential Calculus
. 128
3.2.1
Definition of the Derivative
. 128
3.2.2
Calculating Derivatives
. 135
32.3
Implicit Differentiation
. 138
3.2.4
Tangent lines
. 139
3.2.5
The First Derivative Test and Second
Derivative Test
. 148
32.6
Applied
Max/Min
Problems
. 156
32.7
Antidifferentiation
. 164
3.3
Integral Calculus
.
l68
3.3.1
Area
. 168
332
The Definite Integral
. 174
3.3.3
Approximating Definite Integrals
. 179
3.3.4
Area
. 180
335
Arc Length
. 186
33.6
Solids of Revolution
. 190
3.4
Series
. 201
3.4.1
Introduction to Sequences and Series
. 201
3-4.2
Convergence Tests
. 205
3-4.3
Alternating Series
. 209
З.4.4
Power Series
. 210
3-4.5
Taylor and Maclaurin Series
. 213
3-4.6
Taylor's Theorem
. 217
З.4.7
Other Series
. 220
3.5 Multivariable
Calculus
. 221
35.1
limits of Functions of Two Variables
. 222
35.2
Partial and Directional Derivatives
. 224
35.3
Iterated Integrals
. 238
3.6
Exercises
. 246
CHAPTER
4
Introduction to Lists and Tables
251
4-1
Lists and List Operations
. 251
41.1
Defining lists
. 251
4.1.2
Plotting lists of Points
. 258
4-2
Manipulating lists: More on Part and Map
. 269
4.2.1
More on Graphing lists: Graphing lists of Points
Using Graphics Primitives
. 277
4.2.2
Miscellaneous list Operations
. 283
Contents
I
vii
4.3
Other
Applications
. 283
4.3.1
Approximating lists with Functions
. 283
4.32
Introduction to Fourier Series
. 287
4.33
The Mandelbrot Set and Julia Sets
. 299
4.4
Exercises
. 311
CHAPTER
5
Matrices and Vectors: Topics from
Linear Algebra and Vector Calculus
317
5.1
Nested lists: Introduction to Matrices, Vectors, and
Matrix Operations
. 317
5.1.1
Defining Nested lists, Matrices, and Vectors
. 317
5.1.2
Extracting Elements of Matrices
. 322
5.1.3
Basic Computations with Matrices
. 325
5.1.4
Basic Computations with Vectors
. 329
5.2
Linear Systems of Equations
. 337
5.2.1
Calculating Solutions of linear Systems of
Equations
. 337
5.2.2
Gauss-Jordan Elimination
. 342
5.3
Selected Topics from linear Algebra
. 349
5.3.1
Fundamental Subspaces Associated with
Matrices
. 349
5.32
The Gram-Schmidt Process
. 351
5.33
linear Transformations
. 355
5.3-4
Eigenvalues and Eigenvectors
. 358
5.3.5
Jordan Canonical Form
. 361
5.36
The QR Method
. 364
5.4
Maxima and Minima Using linear Programming
. 366
5.4.1
The Standard Form of a linear Programming
Problem
. 366
5.4.2
The Dual Problem
. 368
5.5
Selected Topics from Vector Calculus
. 374
5.5.1
Vector-Valued Functions
. 374
5.5.2
line Integrals
. 384
5.5.3
Surface Integrals
. 387
5.5.4
A Note on Nonorientability
. 391
5.5-5
More on Tangents, Normals, and Curvature in
72 . 404
5.6
Matrices and Graphics
. 415
5.7
Exercises
. 430
CHAPTER
6
Applications Related to Ordinary and
Partial Differential Equations
435
6.1
First-Order Differential Equations
. 435
6.1.1
Separable Equations
. 435
6.1.2
linear Equations
. 442
vili
I Contents
6.1.3
Nonlinear Equations
. 450
6.1.4
Numerical Methods
. 453
6.2
Second-Order Linear Equations
. 457
6.2.1
Basic Theory
. 457
6.2.2
Constant Coefficients
. 458
6.2.3
Undetermined Coefficients
. 464
6.2.4
Variation of Parameters
. 470
6.3
Higher-Order Linear Equations
. 472
6.3.1
Basic Theory
. 472
6.3.2
Constant Coefficients
. 473
6.3.3
Undetermined Coefficients
. 475
6.3.4
Laplace Transform Methods
. 481
6.3.5
Nonlinear Higher-Order Equations
. 492
6.4
Systems of Equations
. 492
6.4.1
Linear Systems
. 492
6.4.2
Nonhomogeneous Linear Systems
. 505
6.4.3
Nonlinear Systems
. 511
6.5
Some Partial Differential Equations
. 532
6.5.1
The One-Dimensional Wave Equation
. 532
6.5.2
The Two-Dimensional Wave Equation
. 537
6.5.3
Other Partial Differential Equations
. 547
6.6
Exercises
. 550
References
557
Index
559 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Abell, Martha L. 1962- Braselton, James P. 1965- |
| author_GND | (DE-588)130087025 (DE-588)135895197 |
| author_facet | Abell, Martha L. 1962- Braselton, James P. 1965- |
| author_role | aut aut |
| author_sort | Abell, Martha L. 1962- |
| author_variant | m l a ml mla j p b jp jpb |
| building | Verbundindex |
| bvnumber | BV035097490 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.95 |
| callnumber-search | QA76.95 |
| callnumber-sort | QA 276.95 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 601 |
| ctrlnum | (OCoLC)845415216 (DE-599)BVBBV035097490 |
| dewey-full | 510.285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.285 |
| dewey-search | 510.285 |
| dewey-sort | 3510.285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV035097490 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:12:51Z |
| indexdate | 2024-09-10T00:56:06Z |
| institution | BVB |
| isbn | 9780123743183 0123743184 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016765519 |
| oclc_num | 845415216 |
| open_access_boolean | |
| owner | DE-29T DE-92 |
| owner_facet | DE-29T DE-92 |
| physical | XI, 564 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Elsevier Academic Press |
| record_format | marc |
| spelling | Abell, Martha L. 1962- Verfasser (DE-588)130087025 aut Mathematica by example Martha L. Abell and James P. Braselton 4. ed. Amsterdam [u.a.] Elsevier Academic Press 2009 XI, 564 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematica (Computer file) Mathematics / Data processing Datenverarbeitung Mathematik Mathematics Data processing Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Mathematica Programm (DE-588)4268208-3 s 1\p DE-604 Braselton, James P. 1965- Verfasser (DE-588)135895197 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016765519&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 | Abell, Martha L. 1962- Braselton, James P. 1965- Mathematica by example Mathematica (Computer file) Mathematics / Data processing Datenverarbeitung Mathematik Mathematics Data processing Mathematica Programm (DE-588)4268208-3 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4037944-9 |
| title | Mathematica by example |
| title_auth | Mathematica by example |
| title_exact_search | Mathematica by example |
| title_exact_search_txtP | 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 | Mathematica (Computer file) Mathematics / Data processing Datenverarbeitung Mathematik Mathematics Data processing Mathematica Programm (DE-588)4268208-3 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematica (Computer file) Mathematics / Data processing Datenverarbeitung Mathematik Mathematics Data processing Mathematica Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016765519&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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