Applied differential equations: the primary course
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL [u.a.]
CRC Press
2015
|
| Schriftenreihe: | Textbooks in mathematics
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | XVI, 715 S. graph. Darst. |
| ISBN: | 9781439851043 1439851042 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV041215498 | ||
| 003 | DE-604 | ||
| 005 | 20150619 | ||
| 007 | t | ||
| 008 | 130812s2015 d||| |||| 00||| eng d | ||
| 020 | |a 9781439851043 |9 978-1-4398-5104-3 | ||
| 020 | |a 1439851042 |9 1-4398-5104-2 | ||
| 035 | |a (OCoLC)904560234 | ||
| 035 | |a (DE-599)BVBBV041215498 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-83 |a DE-19 |a DE-355 |a DE-824 |a DE-739 | ||
| 084 | |a SK 500 |0 (DE-625)143243: |2 rvk | ||
| 084 | |a 34-01 |2 msc | ||
| 100 | 1 | |a Dobrushkin, Vladimir A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied differential equations |b the primary course |c Vladimir A. Dobrushkin |
| 264 | 1 | |a Boca Raton, FL [u.a.] |b CRC Press |c 2015 | |
| 300 | |a XVI, 715 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Textbooks in mathematics | |
| 490 | 0 | |a A Chapman & Hall book | |
| 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 Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026190142 | ||
Datensatz im Suchindex
| _version_ | 1804150649741377536 |
|---|---|
| adam_text |
Applied Differential Equations: The Primary
Course presents a contemporary treatment of or-
dinary differential equations, including their appli-
cations in engineering and the sciences. The text
enables students majoring in a range of fields to
obtain a solid foundation. Developed as a primary
text for the author’s two-semester course offered
in an applied mathematics department, the text of-
fers a true alternative to texts originally published
for previous generations.
This interesting new approach contains practical techniques for solving the equations as well as cor-
responding codes for numerical solvers. Many examples and exercises help students master effec-
tive solution techniques, including reliable numerical approximations. The author covers traditional
material, along with novel approaches to mathematical modeling that harness the capabilities of
numerical algorithms and popular computer software packages.
ir
Features
• Covers basic and advanced topics in differential equations at a level suitable for an undergraduate course
y A ·. If411 yjr ijw*
• Presents various methods for analyzing, solving, and visualizing ODEs
, ,i I ՛ f!։ ^f ,V*lvi £՛՛.$ i ll՝ 1 ft i!T ՛ ^ ^
• Gives an introduction to several computer software packages, including Maple™, Mathematical,
m
1 i
u
U y
m
fm
MAT1AB®
Numerous examples show students how to model real-world problems
à J Ï3 î I » of Krl ■ TWf .a*
Provides the basic formulas and techniques, making it easy for students to understand the derivations
Contains many exercises throughout each chapter and review questions
1
Connecting calculus, modeling, and advanced topics, this text prepares students for more rigorous study of
differential equations and their applications. Students will learn how to formulate a mathematical model, solve
differential equations analytically and numerically, analyze them qualitatively, and interpret the results.
.1 I t , i
Contents P
List of Symbols xi
Preface xiii
1 Introduction 1
1.1 Motivation ................................................................. 2
1.2 Classification of Differential Equations.................................... 4
1.3 Solutions to Differential Equations......................................... 5
1.4 Particular and Singular Solutions...........................................10
1.5 Direction Fields............................................................13
1.6 Existence and Uniqueness....................................................24
Review Questions for Chapter 1.........................................41
2
First Order Equations
2.1 Separable Equations.......................................................
2.1.1 Autonomous Equations...............................................
2.2 Equations Reducible to Separable Equations................................
2.2.1 Equations with Homogeneous Coefficients............................
2.2.2 Equations with Homogeneous Fractions...............................
2.2.3 Equations writh Linear Coefficients................................
2.3 Exact Differential Equations..............................................
2.4 Simple Integrating Factors................................................
2.5 First Order Linear Differential Equations ................................
2.6 Special Classes of Equations..............................................
2.6.1 The Bernoulli Equation.............................................
2.6.2 The Riccati Equation ..............................................
2.6.3 Equations with the Dependent or Independent Variable Missing.......
2.6.4 Equations Homogeneous with Respect to Their Dependent Variable and
Derivatives........................................................
2.6.5 Equations Solvable for a Variable..................................
45
45
54
61
62
66
73
84
93
100
110
110
114
121
124
126
v
vi Contents
2.7 Qualitative Analysis....................................................129
2.7Л Bifurcation Points..................................................135
2.7.2 Validity Intervals of Autonomous Equations........................139
Summary for Chapter 2........................................................147
Review Questions for Chapter 2............................................. 149
3 Numerical Methods 155
3.1 Difference Equations....................................................156
3.2 Euler’s Methods .......................................................165
3.3 The Polynomial Approximation............................................179
3.4 Error Estimates.........................................................187
3.5 The Runge-Kutta Methods.................................................197
Summary for Chapter 3........................................................206
Review Questions for Chapter 3...............................................207
4 Second and Higher Order Linear Differential Equations 211
4.1 Second and Higher Order Differential Equations..........................212
4.1.1 Linear Operators..................................................214
4.1.2 Exact Equations and Integrating Factors ..........................216
4.1.3 Change of Variables...............................................210
4.2 Linear Independence and Wronskians......................................223
4.3 The Fundamental Set of Solutions ......................................230
4.4 Equations with Constant Coefficients....................................234
4.5 Complex Roots......................................................... 239
4.6 Repeated Roots. Reduction of Order......................................245
4.6.1 Reduction of Order.............................................. 248
4.7 Nonhomogeneous Equations................................................252
4.7.1 The Method of Undetermined Coefficients...........................255
4.8 Variation of Parameters............................................... 268
4.9 Bessel Equations...................................................... 275
4.9.1 Parametric Bessel Equation..................................... * .278
4.9.2 Bessel Functions of Half-Integer Order............................279
4.9.3 Related Differential Equations ...................................280
Summary for Chapter 4........................................................285
Review Questions for Chapter 4...............................................288
5 Laplace Transforms 301
5.1 The Laplace Transform ..................................................302
5.2 Properties of the Laplace Transform.....................................316
Contents
Vil
5.3 Discontinuous and Impulse Functions......................................326
5.4 The Inverse Laplace Transform............................................338
5.4.1 Partial Fraction Decomposition....................................339
5.4.2 Convolution Theorem...............................................343
5.4.3 The Residue Method................................................345
5.5 Homogeneous Differential Equations.......................................351
5.5.1 Equations with Variable Coefficients..............................355
5.6 Nonhomogeneous Differential Equations....................................358
5.6.1 Differential Equations with Intermittent Forcing Functions .......362
Summary for Chapter 5........................................................370
Review Questions for Chapter 5...............................................374
6 Introduction to Systems of ODEs 381
6.1 Some ODE Models..........................................................381
6.1.1 RLC-Circuits......................................................382
6.1.2 Spring-Mass Systems...............................................384
6.1.3 The Euler -Lagrange Equation .....................................385
6.1.4 Pendulum..........................................................386
6.1.5 Laminated Material................................................391
6.1.6 Flow Problems.....................................................391
6.2 Matrices.................................................................398
6.3 Linear Systems of First Order ODEs.......................................406
6.4 Reduction to a Single ODE................................................410
6.5 Existence and Uniqueness.................................................417
Summary for Chapter 6........................................................420
Review Questions for Chapter 6...............................................421
7 Topics from Linear Algebra
7.1 The Calculus of Matrix Functions.........
7.2 Inverses and Determinants................
7.2.1 Solving Linear Equations..........
7.3 Eigenvalues arid Eigenvectors............
7.4 Diagonalization..........................
7.5 Sylvester’s Formula......................
7.6 The Resolvent Method.....................
7.7 The Spectral Decomposition Method . . . .
Summary for Chapter 7........................
Review Questions for Chapter 7...............
423
423
426
431
434
440
449
454
461
473
476
viii Contents
8 Systems of Linear Differential Equations 481
8.1 Systems of Linear Equations..............................................482
8.1.1 The Euler Vector Equations........................................489
8.2 Constant Coefficient Homogeneous Systems.................................491
8.2.1 Simple Real Eigenvalues...........................................496
8.2.2 Complex Eigenvalues...............................................499
8.2.3 Repeated Eigenvalues..............................................501
8.2.4 Qualitative Analysis of Linear Systems............................504
8.3 Variation of Parameters..................................................509
8.3.1 Equations with Constant Coefficients..............................511
8.4 Method of Undetermined Coefficients......................................517
8.5 The Laplace Transformation...............................................521
8.6 Second Order Linear Systems..............................................525
Summary for Chapter 8.........................................................532
Review Questions for Chapter 8................................................535
9 Qualitative Theory of Differential Equations 539
9.1 Autonomous Systems.......................................................540
9.1.1 Two-Dimensional Autonomous Equations............................542
9.2 Linearization............................................................549
9.2.1 Two-Dimensional Autonomous Equations............................551
9.2.2 Scalar Equations..................................................555
9.3 Population Models........................................................557
9.3.1 Competing Species.................................................558
9.3.2 Predator-Prev Equations ..........................................563
9.3.3 Other Population Models...........................................568
9.4 Conservative Systems ....................................................573
9.4.1 Hamiltonian Systems...............................................575
9.5 Lyapunov s Second Method.................................................581
9.6 Periodic Solutions ......................................................589
9.6.1 Equations with Periodic Coefficients..............................596
Summary for Chapter 9.........................................................600
Review Questions for Chapter 9................................................601
10 Orthogonal Expansions 609
10.1 Sturm—Liouville Problems.................................................609
10.2 Orthogonal Expansions ...................................................618
10.3 Fourier Series...........................................................625
10.3.1 Music as Motivation...............................................625
Contents ix
10.3.2 Sturm-Liouville Periodic Problem................................628
10.3.3 Fourier Series..................................................629
10.4 Convergence of Fourier Series.........................................637
10.4.1 Complex Fourier Series .........................................642
10.4.2 The Gibbs Phenomenon............................................646
10.5 Even and Odd Functions................................................650
Summary for Chapter 10 659
Review Questions for Chapter 10............................................660
11 Partial Differential Equations 665
11.1 Separation of Variables for the Heat Equation.........................666
11.1.1 Two-Dimensional Heat Equation...................................672
11.2 Other Heat Conduction Problems........................................675
11.3 Wave Equation.........................................................680
11.3.1 Transverse Vibrations of Beams..................................685
11.4 Laplace Equation......................................................689
11.4.1 Laplace Equation in Polar Coordinates...........................691
Summary for Chapter 11 696
Review Questions for Chapter 11............................................697
Bibliography 701
Index
705
|
| any_adam_object | 1 |
| author | Dobrushkin, Vladimir A. |
| author_facet | Dobrushkin, Vladimir A. |
| author_role | aut |
| author_sort | Dobrushkin, Vladimir A. |
| author_variant | v a d va vad |
| building | Verbundindex |
| bvnumber | BV041215498 |
| classification_rvk | SK 500 |
| ctrlnum | (OCoLC)904560234 (DE-599)BVBBV041215498 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01700nam a2200373 c 4500</leader><controlfield tag="001">BV041215498</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150619 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130812s2015 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781439851043</subfield><subfield code="9">978-1-4398-5104-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1439851042</subfield><subfield code="9">1-4398-5104-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)904560234</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV041215498</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 500</subfield><subfield code="0">(DE-625)143243:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dobrushkin, Vladimir A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Applied differential equations</subfield><subfield code="b">the primary course</subfield><subfield code="c">Vladimir A. Dobrushkin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton, FL [u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 715 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Textbooks in mathematics</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">A Chapman & Hall book</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-026190142</subfield></datafield></record></collection> |
| id | DE-604.BV041215498 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:42:17Z |
| institution | BVB |
| isbn | 9781439851043 1439851042 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026190142 |
| oclc_num | 904560234 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-824 DE-739 |
| owner_facet | DE-703 DE-83 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-824 DE-739 |
| physical | XVI, 715 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Textbooks in mathematics A Chapman & Hall book |
| spelling | Dobrushkin, Vladimir A. Verfasser aut Applied differential equations the primary course Vladimir A. Dobrushkin Boca Raton, FL [u.a.] CRC Press 2015 XVI, 715 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics A Chapman & Hall book Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dobrushkin, Vladimir A. Applied differential equations the primary course Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Applied differential equations the primary course |
| title_auth | Applied differential equations the primary course |
| title_exact_search | Applied differential equations the primary course |
| title_full | Applied differential equations the primary course Vladimir A. Dobrushkin |
| title_fullStr | Applied differential equations the primary course Vladimir A. Dobrushkin |
| title_full_unstemmed | Applied differential equations the primary course Vladimir A. Dobrushkin |
| title_short | Applied differential equations |
| title_sort | applied differential equations the primary course |
| title_sub | the primary course |
| topic | Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190142&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dobrushkinvladimira applieddifferentialequationstheprimarycourse |