Differential equations with Mathematica: updated for Mathematica 6
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Hoboken
Wiley
2009
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 271 S. graph. Darst. |
| ISBN: | 9780471773160 |
Internformat
MARC
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| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
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| 050 | 0 | |a QA371.5.D37 | |
| 084 | |a ST 601 |0 (DE-625)143682: |2 rvk | ||
| 245 | 1 | 0 | |a Differential equations with Mathematica |b updated for Mathematica 6 |c Brian R. Hunt ... |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Hoboken |b Wiley |c 2009 | |
| 300 | |a VIII, 271 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 630 | 0 | 4 | |a Mathematica (Computer file) |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Differential equations |x Data processing | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematica 6 |0 (DE-588)7581228-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 1 | |a Mathematica 6 |0 (DE-588)7581228-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hunt, Brian R. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016405721 | ||
Datensatz im Suchindex
| _version_ | 1804137506470363136 |
|---|---|
| adam_text | Contents
Preface
v
1
Introduction
1
1.1
Guiding Philosophy
.............................. 1
1.2
Student s Guide
................................ 3
1.3
Instructor s Guide
............................... 4
1.3.1
Mathematica
............................. 4
1.3.2
ODE Chapters
............................ 5
1.3.3
Computer Problem Sets
....................... 5
1.4
A Word about Software Versions
....................... 6
2
Getting Started with
Mathematica
7
2.1
Platforms and Versions
............................ 7
2.2
Installation
.................................. 8
2.3
Starting
Mathematica
............................. 8
2.4
Mathematica
Input
.............................. 9
2.5
Online Help
.................................. 10
2.6
Ending a Session
............................... 11
3
Doing Mathematics with
Mathematica
13
3.1
Arithmetic
................................... 13
3.2
Recovering from Problems
.......................... 14
3.2.1
Errors in Input
............................ 14
3.2.2
Aborting Calculations
........................ 15
3.3
Symbolic Computation
............................ 15
3.3.1
Assignments
............................. 16
3.3.2
Suppressing Output
.......................... 17
3.3.3
Referring to Previous Output
..................... 17
3.4
Functions and Expressions
.......................... 18
3.4.1
Built-in Functions
.......................... 18
3.4.2
User-defined Functions
........................ 18
3.4.3
Expressions
.............................. 19
3.5
Lists and Tables
................................ 19
3.5.1
Extracting Parts of Lists
....................... 19
v
vj
Contents
3.5.2
Combining Lists
...........................20
3.5.3
Tables of Values
...........................20
3.6
Solving Equations
...............................21
3.7
Graphics
.................................... 23
3.7.1
Basic Plotting
............................. 23
3.7.2
Modifying Graphs
.......................... 24
3.7.3
Plotting Multiple Curves
....................... 24
3.7.4
Plotting Data Lists
.......................... 25
3.7.5
Parametric Plots
........................... 26
3.7.6
ContourPlots
............................. 26
3.8
Calculus
.................................... 27
3.9
Packages
................................... 29
3.10
Some Tips and Reminders
.......................... 29
4
Using
Mathematica
Notebooks
31
4.1
The Kernel and the Front End
......................... 31
4.2
The Notebook
................................. 32
4.2.1
Quitting the Kernel
.......................... 33
4.2.2
Cells
................................. 33
4.2.3
Cell Hierarchy
............................ 33
4.2.4
Pointers and Insertion Points
..................... 34
4.2.5
Manipulating Cells
.......................... 35
4.2.6
Mathematical Typesetting
...................... 35
4.2.7
Displaying and Printing
Mathematica
Notebooks
.......... 36
4.2.8
Preparing Homework Solutions
................... 37
Problem Set A: Practice with
Mathematica
41
5
Solutions of Differential Equations
45
5.1
Finding Symbolic Solutions
......................... 45
5.2
Existence and Uniqueness
.......................... 47
5.3
Stability of Differential Equations
...................... 49
5.4
Different Types of Symbolic Solutions
.................... 53
6
A Qualitative Approach to Differential Equations
59
6.1
Direction Field for a First Order Linear Equation
.............. 59
6.2
Direction Field for a Non-Linear Equation
.................. 61
6.3
Autonomous Equations
............................ 63
6.3.1
Examples of Autonomous Equations
................. 65
Problem Set B: First Order Equations
69
Contents
vii
7
Numerical Methods
79
7.1
Numerical Solutions Using
Mathematica
................... 80
7.2
Some Numerical Methods
.......................... 83
7.2.1
The
Euler
Method
.......................... 83
7.2.2
The Improved
Euler
Method
..................... 86
7.2.3
The Runge-Kutta Method
...................... 88
7.2.4
The Adams Methods
......................... 88
7.2.5
Backwards Differentiation Formulas
................. 89
7.3
Inside NDSolve
............................... 90
7.4
Round-off Error
................................ 90
7.5
Controlling the Error in NDSolve
...................... 91
7.6
Reliability of Numerical Methods
...................... 92
8
Features of
Mathematica
97
8.1
Functions and Expressions
.......................... 97
8.2
Pure Functions
................................ 98
8.3
Clearing Values
................................ 99
8.4
Managing Memory
..............................100
8.5
The Replacement Operator and Transformation Rules
............101
8.6
Equations
ví.
Assignments
..........................102
8.7
Differentiation
.................................102
8.8
Vectors and Matrices
.............................103
8.8.1
Solving Linear Systems
.......................104
8.8.2
Calculating Eigenvalues and Eigenvectors
..............105
8.9
Graphics
....................................106
8.9.1
Options for Plots
...........................106
8.9.2
Plotting Vector Fields
.........................108
8.9.3
Redrawing Plots
...........................109
8.9.4
Editing Figures
............................109
8.10
The Evaluate Command
..........................
Ill
8.11
More about DSol
ve
.............................112
8.12
More about
řrosolve
............................112
8.12.1
Event Detection
............................114
8.13
Troubleshooting
................................116
8.13.1
The Most Common Mistakes
.....................116
8.13.2
Error and Warning Messages
.....................117
8.13.3
Recovering from Errors
.......................119
Problem Set C: Numerical Solutions
121
viu
Contents
9
Solving and Analyzing Second Order Linear Equations
129
9.1
Second Order Equations with
Mathematica
.................131
9.2
Boundary Value Problems
..........................133
9.3
Comparison Methods
.............................135
9.3.1
The Interlacing of Zeros
.......................137
9.3.2
Proof of the Sturm Comparison Theorem
..............138
9.4
A Geometric Method
.............................138
9.4.1
The Constant Coefficient Case
....................139
9.4.2
The Variable Coefficient Case
....................140
9.4.3
Airy
s
Equation
............................141
9.4.4
Bessel s Equation
...........................142
9.4.5
Other Equations
...........................143
Problem Set D: Second Order Equations
145
10
Series Solutions
159
10.1
Series Solutions
................................160
10.2
Singular Points
................................163
11
Laplace Transforms
167
11.1
Differential Equations and Laplace Transforms
...............169
11.2
Discontinuous Functions
...........................172
11.3
Differential Equations with Discontinuous Forcing
.............175
Problem Set E: Series Solutions and Laplace Transforms
177
12
Higher Order Equations and Systems of First Order Equations
189
12.1
Higher Order Linear Equations
........................190
12.2
Systems of First Order Equations
.......................191
12.2.1
Linear First Order Systems
......................192
12.2.2
Using
Mathematica
to Find Eigenpairs
...............194
12.3
Phase Portraits
................................198
12.3.1
Plotting a Single Trajectory
.....................199
12.3.2
Plotting Several Trajectories
.....................199
12.3.3
Numerical Solutions of First Order Systems
.............201
13
Qualitative Theory for Systems of Differential Equations
205
Problem Set F: Systems of Differential Equations
213
Glossary
229
Sample Solutions
239
Index
261
|
| adam_txt |
Contents
Preface
v
1
Introduction
1
1.1
Guiding Philosophy
. 1
1.2
Student's Guide
. 3
1.3
Instructor's Guide
. 4
1.3.1
Mathematica
. 4
1.3.2
ODE Chapters
. 5
1.3.3
Computer Problem Sets
. 5
1.4
A Word about Software Versions
. 6
2
Getting Started with
Mathematica
7
2.1
Platforms and Versions
. 7
2.2
Installation
. 8
2.3
Starting
Mathematica
. 8
2.4
Mathematica
Input
. 9
2.5
Online Help
. 10
2.6
Ending a Session
. 11
3
Doing Mathematics with
Mathematica
13
3.1
Arithmetic
. 13
3.2
Recovering from Problems
. 14
3.2.1
Errors in Input
. 14
3.2.2
Aborting Calculations
. 15
3.3
Symbolic Computation
. 15
3.3.1
Assignments
. 16
3.3.2
Suppressing Output
. 17
3.3.3
Referring to Previous Output
. 17
3.4
Functions and Expressions
. 18
3.4.1
Built-in Functions
. 18
3.4.2
User-defined Functions
. 18
3.4.3
Expressions
. 19
3.5
Lists and Tables
. 19
3.5.1
Extracting Parts of Lists
. 19
v
vj
Contents
3.5.2
Combining Lists
.20
3.5.3
Tables of Values
.20
3.6
Solving Equations
.21
3.7
Graphics
. 23
3.7.1
Basic Plotting
. 23
3.7.2
Modifying Graphs
. 24
3.7.3
Plotting Multiple Curves
. 24
3.7.4
Plotting Data Lists
. 25
3.7.5
Parametric Plots
. 26
3.7.6
ContourPlots
. 26
3.8
Calculus
. 27
3.9
Packages
. 29
3.10
Some Tips and Reminders
. 29
4
Using
Mathematica
Notebooks
31
4.1
The Kernel and the Front End
. 31
4.2
The Notebook
. 32
4.2.1
Quitting the Kernel
. 33
4.2.2
Cells
. 33
4.2.3
Cell Hierarchy
. 33
4.2.4
Pointers and Insertion Points
. 34
4.2.5
Manipulating Cells
. 35
4.2.6
Mathematical Typesetting
. 35
4.2.7
Displaying and Printing
Mathematica
Notebooks
. 36
4.2.8
Preparing Homework Solutions
. 37
Problem Set A: Practice with
Mathematica
41
5
Solutions of Differential Equations
45
5.1
Finding Symbolic Solutions
. 45
5.2
Existence and Uniqueness
. 47
5.3
Stability of Differential Equations
. 49
5.4
Different Types of Symbolic Solutions
. 53
6
A Qualitative Approach to Differential Equations
59
6.1
Direction Field for a First Order Linear Equation
. 59
6.2
Direction Field for a Non-Linear Equation
. 61
6.3
Autonomous Equations
. 63
6.3.1
Examples of Autonomous Equations
. 65
Problem Set B: First Order Equations
69
Contents
vii
7
Numerical Methods
79
7.1
Numerical Solutions Using
Mathematica
. 80
7.2
Some Numerical Methods
. 83
7.2.1
The
Euler
Method
. 83
7.2.2
The Improved
Euler
Method
. 86
7.2.3
The Runge-Kutta Method
. 88
7.2.4
The Adams Methods
. 88
7.2.5
Backwards Differentiation Formulas
. 89
7.3
Inside NDSolve
. 90
7.4
Round-off Error
. 90
7.5
Controlling the Error in NDSolve
. 91
7.6
Reliability of Numerical Methods
. 92
8
Features of
Mathematica
97
8.1
Functions and Expressions
. 97
8.2
Pure Functions
. 98
8.3
Clearing Values
. 99
8.4
Managing Memory
.100
8.5
The Replacement Operator and Transformation Rules
.101
8.6
Equations
ví.
Assignments
.102
8.7
Differentiation
.102
8.8
Vectors and Matrices
.103
8.8.1
Solving Linear Systems
.104
8.8.2
Calculating Eigenvalues and Eigenvectors
.105
8.9
Graphics
.106
8.9.1
Options for Plots
.106
8.9.2
Plotting Vector Fields
.108
8.9.3
Redrawing Plots
.109
8.9.4
Editing Figures
.109
8.10
The Evaluate Command
.
Ill
8.11
More about DSol
ve
.112
8.12
More about
řrosolve
.112
8.12.1
Event Detection
.114
8.13
Troubleshooting
.116
8.13.1
The Most Common Mistakes
.116
8.13.2
Error and Warning Messages
.117
8.13.3
Recovering from Errors
.119
Problem Set C: Numerical Solutions
121
viu
Contents
9
Solving and Analyzing Second Order Linear Equations
129
9.1
Second Order Equations with
Mathematica
.131
9.2
Boundary Value Problems
.133
9.3
Comparison Methods
.135
9.3.1
The Interlacing of Zeros
.137
9.3.2
Proof of the Sturm Comparison Theorem
.138
9.4
A Geometric Method
.138
9.4.1
The Constant Coefficient Case
.139
9.4.2
The Variable Coefficient Case
.140
9.4.3
Airy'
s
Equation
.141
9.4.4
Bessel's Equation
.142
9.4.5
Other Equations
.143
Problem Set D: Second Order Equations
145
10
Series Solutions
159
10.1
Series Solutions
.160
10.2
Singular Points
.163
11
Laplace Transforms
167
11.1
Differential Equations and Laplace Transforms
.169
11.2
Discontinuous Functions
.172
11.3
Differential Equations with Discontinuous Forcing
.175
Problem Set E: Series Solutions and Laplace Transforms
177
12
Higher Order Equations and Systems of First Order Equations
189
12.1
Higher Order Linear Equations
.190
12.2
Systems of First Order Equations
.191
12.2.1
Linear First Order Systems
.192
12.2.2
Using
Mathematica
to Find Eigenpairs
.194
12.3
Phase Portraits
.198
12.3.1
Plotting a Single Trajectory
.199
12.3.2
Plotting Several Trajectories
.199
12.3.3
Numerical Solutions of First Order Systems
.201
13
Qualitative Theory for Systems of Differential Equations
205
Problem Set F: Systems of Differential Equations
213
Glossary
229
Sample Solutions
239
Index
261 |
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| any_adam_object_boolean | 1 |
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| bvnumber | BV023219795 |
| callnumber-first | Q - Science |
| callnumber-label | QA371 |
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| ctrlnum | (OCoLC)308007205 (DE-599)BVBBV023219795 |
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| id | DE-604.BV023219795 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:15:30Z |
| indexdate | 2024-07-09T21:13:23Z |
| institution | BVB |
| isbn | 9780471773160 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016405721 |
| oclc_num | 308007205 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | VIII, 271 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| spelling | Differential equations with Mathematica updated for Mathematica 6 Brian R. Hunt ... 3. ed. Hoboken Wiley 2009 VIII, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematica (Computer file) Datenverarbeitung Differential equations Data processing Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematica 6 (DE-588)7581228-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Mathematica 6 (DE-588)7581228-9 s DE-604 Hunt, Brian R. Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Differential equations with Mathematica updated for Mathematica 6 Mathematica (Computer file) Datenverarbeitung Differential equations Data processing Differentialgleichung (DE-588)4012249-9 gnd Mathematica 6 (DE-588)7581228-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)7581228-9 |
| title | Differential equations with Mathematica updated for Mathematica 6 |
| title_auth | Differential equations with Mathematica updated for Mathematica 6 |
| title_exact_search | Differential equations with Mathematica updated for Mathematica 6 |
| title_exact_search_txtP | Differential equations with Mathematica updated for Mathematica 6 |
| title_full | Differential equations with Mathematica updated for Mathematica 6 Brian R. Hunt ... |
| title_fullStr | Differential equations with Mathematica updated for Mathematica 6 Brian R. Hunt ... |
| title_full_unstemmed | Differential equations with Mathematica updated for Mathematica 6 Brian R. Hunt ... |
| title_short | Differential equations with Mathematica |
| title_sort | differential equations with mathematica updated for mathematica 6 |
| title_sub | updated for Mathematica 6 |
| topic | Mathematica (Computer file) Datenverarbeitung Differential equations Data processing Differentialgleichung (DE-588)4012249-9 gnd Mathematica 6 (DE-588)7581228-9 gnd |
| topic_facet | Mathematica (Computer file) Datenverarbeitung Differential equations Data processing Differentialgleichung Mathematica 6 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT huntbrianr differentialequationswithmathematicaupdatedformathematica6 |