Elementary differential equations with linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Acad. Pr.
1982
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 518 S. |
| ISBN: | 0125739451 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elementary differential equations with linear algebra |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York u.a. |b Acad. Pr. |c 1982 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
one
Introduction to Differential Equations
1.1 Introduction 1
1.2 Separable Equations 9
1.3 Exact Equations 17
1.4 First Order Linear Equations 24
1.5 Orthogonal Trajectories 29
1.6 Radioactive Decay 33
1.7 Mixing Problems 37
1.8 Population Growth 39
1.9 Economic Models 41
1.10 Cooling; The Rate of a Chemical Reaction 45
1.11 Two Special Types of Second Order Equations 50
1.12 Falling Bodies 54
1.13 Some Theoretical Matters 63
:WO
Matrices and Determinants
2.1 Systems of Linear Equations 73
2.2 Homogeneous Systems 86
2.3 Applications Involving Systems of Equations 90
2.4 Matrices and Vectors 95
2.5 Matrix Multiplication 100
2.6 Inner Product and Length 107
2.7 Some Special Matrices 112
2.8 Determinants 117
2.9 Properties of Determinants 122
2.10 Cofactors 128
2.11 Cramer s Rule 131
2.12 The Inverse of a Matrix 138
v
vi Contents
three
Vector Spaces and Linear Transformations
3.1 Vector Spaces 147
3.2 Subspaces 152
3.3 Linear Dependence 156
3.4 Wronskians 161
3.5 Dimension 167
3.6 Orthogonal Bases 170
3.7 Linear Transformations 174
3.8 Properties of Linear Transformations 178
3.9 Differential Operators 182
four
Characteristic Values
4.1 Characteristic Values 191
4.2 An Application: Population Growth 196
4.3 Diagonalization 199
4.4 Real Symmetric Matrices 203
4.5 Functions of Matrices 206
five
Linear Differential Equations
5.1 Introduction 213
5.2 Polynomial Operators 218
5.3 Complex Solutions 224
5.4 Equations with Constant Coefficients 230
5.5 Cauchy Euler Equations 236
5.6 Nonhomogeneous Equations 242
5.7 The Method of Undetermined Coefficients 245
5.8 Variation of Parameters 256
5.9 Simple Harmonic Motion 265
5.10 Electric Circuits 274
SIX
Systems of Differential Equations
6.1 Introduction 283
6.2 First Order Systems 288
Contents vii
6.3 Linear Systems with Constant Coefficients 292
6.4 Matrix Formulation of Linear Systems 301
6.5 Fundamental Sets of Solutions 306
6.6 Solutions by Characteristic Values 313
6.7 Repeated Characteristic Values 317
6.8 Series of Matrices 321
6.9 The Exponential Matrix Function 321
6.10 A Matrix Method 332
6.11 Nonhomogeneous Linear Systems 340
6.12 Mechanical Systems 346
6.13 The Two Body Problem 351
6.14 Electric Circuits 358
6.15 Some Problems from Biology 361
Series Solutions
7.1 Power Series 367
7.2 Taylor Series 373
7.3 Ordinary Points 376
7.4 Singular Points 383
7.5 The Case of Equal Exponents 39/
7.6 The Case when the Exponents Differ by an Integer 396
7.7 The Point at Infinity 402
7.8 Legendre Polynomials 404
7.9 Bessel Functions 409
earn
Numerical Methods
8.1 The Euler Method 419
8.2 Taylor Series Methods 426
8.3 Runge Kutta Methods 430
8.4 A Multi Step Method 434
Laplace Transforms
9.1 The Laplace Transform 443
9.2 Functions of Exponential Order 448
viii Contents
9.3 Properties of Laplace Transforms 452
9.4 Inverse Transforms 457
9.5 Applications to Differential Equations 462
9.6 Functions with Discontinuities 468
References 481
Answers to Selected Exercises 483
Index 515
|
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| indexdate | 2024-07-09T16:03:29Z |
| institution | BVB |
| isbn | 0125739451 |
| language | English |
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| physical | IX, 518 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Acad. Pr. |
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| spelling | Rabenstein, Albert Louis Verfasser aut Elementary differential equations with linear algebra 3. ed. New York u.a. Acad. Pr. 1982 IX, 518 S. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Équations différentielles Algebras, Linear Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Lineare Algebra (DE-588)4035811-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331531&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rabenstein, Albert Louis Elementary differential equations with linear algebra Algèbre linéaire Équations différentielles Algebras, Linear Differential equations Differentialgleichung (DE-588)4012249-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4035811-2 |
| title | Elementary differential equations with linear algebra |
| title_auth | Elementary differential equations with linear algebra |
| title_exact_search | Elementary differential equations with linear algebra |
| title_full | Elementary differential equations with linear algebra |
| title_fullStr | Elementary differential equations with linear algebra |
| title_full_unstemmed | Elementary differential equations with linear algebra |
| title_short | Elementary differential equations with linear algebra |
| title_sort | elementary differential equations with linear algebra |
| topic | Algèbre linéaire Équations différentielles Algebras, Linear Differential equations Differentialgleichung (DE-588)4012249-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Équations différentielles Algebras, Linear Differential equations Differentialgleichung Lineare Algebra |
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