Differential equations: a primer for scientists and engineers
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2013
|
| Schriftenreihe: | Springer Undergraduate Texts in Mathematics and Technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 263 S. graph. Darst. |
| ISBN: | 9781461472964 9781461472971 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV040978512 | ||
| 003 | DE-604 | ||
| 005 | 20171204 | ||
| 007 | t | ||
| 008 | 130502s2013 d||| |||| 00||| eng d | ||
| 020 | |a 9781461472964 |9 978-1-4614-7296-4 | ||
| 020 | |a 9781461472971 |9 978-1-4614-7297-1 | ||
| 035 | |a (OCoLC)854699972 | ||
| 035 | |a (DE-599)BVBBV040978512 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-355 |a DE-19 |a DE-92 |a DE-83 | ||
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| 100 | 1 | |a Constanda, Christian |d 1944- |e Verfasser |0 (DE-588)112608027 |4 aut | |
| 245 | 1 | 0 | |a Differential equations |b a primer for scientists and engineers |c Christian Constanda |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2013 | |
| 300 | |a XV, 263 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer Undergraduate Texts in Mathematics and Technology | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Difference equations | |
| 650 | 4 | |a Functional equations | |
| 650 | 4 | |a Difference and Functional Equations | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 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=025956558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025956558 | ||
Datensatz im Suchindex
| _version_ | 1804150296370216960 |
|---|---|
| adam_text | Contents
Introduction
1
LI Calculus Prerequisites
............................................ 1
1.2
Differential Equations and Their Solutions
.......................... 3
1.3
Initial and Boundary Conditions
.................................. 6
1.4
Classification of Differential Equations
............................. 9
First-Order Equations
15
2.1
Separable Equations
............................................. 15
2.2
Linear Equations
................................................ 20
2.3
Homogeneous Polar Equations
.................................... 24
2.4
Bernoulli Equations
.............................................
2G
2.5
Riccati Equations
............................................... 28
2.6
Exact Equations
................................................ 30
2.7
Existence and Uniqueness Theorems
............................... 35
2.8
Direction Fields
................................................. 40
Mathematical Models with First-Order Equations
41
3.1
Models with Separable Equations
.................................. 41
3.2
Models with Linear Equations
..................................... 44
3.3
Autonomous Equations
........................................... 49
Linear Second-Order Equations
61
4.1
Mathematical Models with Second-Order Equations
................. 61
4.2
Algebra Prerequisites
............................................ 62
4.3
Homogeneous Equations
.......................................... 67
4.3.1
Initial Value Problems
..................................... 67
4.3.2
Boundary Value Problems
.................................. 70
4.4
Homogeneous Equations with Constant Coefficients
.................. 71
4.4.1
Real and Distinct Characteristic Roots
....................... 72
4.4.2
Repeated Characteristic Roots
.............................. 74
4.4.3
Complex Conjugate Characteristic Roots
..................... 77
4.5
NonhomogeneoiLS Equations
...................................... 80
4.5.1
Method of Undetermined Coefficients: Simple Cases
........... 81
4.5.2
Method of Undetermined Coefficients: General Case
........... 88
4.5.3
Method of Variation of Parameters
.......................... 94
Contents
4.6 Cauchy-Euler
Equations .........................................
97
4.7
Nonlinear Equations
.............................................100
Mathematical Models with Second-Order Equations
103
5.1
Free Mechanical Oscillations
...................................... 103
5.1.1
Undamped Free Oscillations
................................ 103
5.1.2
Damped Free Oscillations
.................................. 106
5.2
Forced Mechanical Oscillations
.................................... 110
5.2.1
Undamped Forced Osculations
.............................. 110
5.2.2
Damped Forced Oscillations
................................ 112
5.3
Electrical Vibrations
............................................. 114
Higher-Order Linear Equations
117
6.1
Modeling with Higher-Order Equations
.............................117
6.2
Algebra Prerequisites
............................................117
6.2.1
Matrices and Determinants of Higher Order
..................118
6.2.2
Systems of Linear Algebraic Equations
.......................119
6.2.3
Linear Independence and the Wronskian
.....................124
6.3
Homogeneous Differential Equations
...............................126
64
Nonhomogeneous Equations
......................................130
6.4.1
Method of Undetermined Coefficients
........................130
6.4.2
Method of Variation of Parameters
..........................134
Systems of Differential Equations
137
7.1
Modeling with Systems of Equations
............................... 137
7.2
Algebra Prerequisites
............................................139
7.2.1
Operations with Matrices
...................................139
7.2.2
Linear Independence and the Wronskian
.....................145
7.2.3
Eigenvalues and Eigenvectors
...............................147
7.3
Systems of First-Order Differential Equations
.......................151
7.4
Homogeneous Linear Systems with Constant Coefficients
.............154
7.4.1
Real and Distinct Eigenvalues
...............................155
7.4.2
Complex Conjugate Eigenvalues
.............................161
7.4.3
Repeated Eigenvalues
......................................165
7.5
Other Features of Homogeneous Linear Systems
.....................173
7.6
Nonhomogeneous Linear Systems
..................................178
The Laplace Transformation
187
8.1
Definition and Basic Properties
...................................187
8.2
Further Properties
...............................................194
8.3
Solution of IVPs for Single Equations
..............................199
8.3.1
Continuous Forcing Terms
..................................199
8.3.2
Piecewise Continuous Forcing Terms
.........................204
8.3.3
Forcing Terms with the Dirac Delta
..........................208
8.3.4
Equations with Variable Coefficients
.........................212
8.4
Solution of IVPs for Systems
......................................215
Series Solutions
221
9.1
Power Series
....................................................221
9.2
Series Solution Near an Ordinary Point
............................222
9.3
Singular Points
..................................................229
Contents xiii
9.4
Solution Near a Regular Singular Point
.............................231
9.4.1
Distinct Roots That Do Not Differ by an Integer
..............232
9.4.2
Equal Roots
..............................................236
9.4.3
Distinct Roots Differing by an Integer
........................241
A Algebra Techniques
249
A.I Partial Fractions
................................................249
A.
2
Synthetic Division
...............................................251
В
Calculus Techniques
253
B.I Sign of a Function
...............................................253
B.2 Integration by Parts
.............................................253
B.3 Integration by Substitution
.......................................254
С
Table of Laplace Transforms
255
D
The Greek Alphabet
257
Further Reading
259
Index
261
|
| any_adam_object | 1 |
| author | Constanda, Christian 1944- |
| author_GND | (DE-588)112608027 |
| author_facet | Constanda, Christian 1944- |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.75 515.625 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040978512 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:36:40Z |
| institution | BVB |
| isbn | 9781461472964 9781461472971 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025956558 |
| oclc_num | 854699972 |
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| physical | XV, 263 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
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| series2 | Springer Undergraduate Texts in Mathematics and Technology |
| spelling | Constanda, Christian 1944- Verfasser (DE-588)112608027 aut Differential equations a primer for scientists and engineers Christian Constanda New York, NY [u.a.] Springer 2013 XV, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Undergraduate Texts in Mathematics and Technology Mathematics Difference equations Functional equations Difference and Functional Equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025956558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Constanda, Christian 1944- Differential equations a primer for scientists and engineers Mathematics Difference equations Functional equations Difference and Functional Equations Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Differential equations a primer for scientists and engineers |
| title_auth | Differential equations a primer for scientists and engineers |
| title_exact_search | Differential equations a primer for scientists and engineers |
| title_full | Differential equations a primer for scientists and engineers Christian Constanda |
| title_fullStr | Differential equations a primer for scientists and engineers Christian Constanda |
| title_full_unstemmed | Differential equations a primer for scientists and engineers Christian Constanda |
| title_short | Differential equations |
| title_sort | differential equations a primer for scientists and engineers |
| title_sub | a primer for scientists and engineers |
| topic | Mathematics Difference equations Functional equations Difference and Functional Equations Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Difference equations Functional equations Difference and Functional Equations Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025956558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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