Holdings: Ordinary differential equations

Ordinary differential equations: example-driven, including Maple Code

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Bibliographic Details
Main Author:	Precup, Radu 1955- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2018]
Series:	De Gruyter Graduate
Subjects:	Maple > Programm Gewöhnliche Differentialgleichung Algorithmus Fachhochschul-/Hochschulausbildung
Online Access:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110447422&searchTitles=true Inhaltsverzeichnis
Physical Description:	XIII, 221 Seiten Illustrationen, Diagramme 24 cm x 17 cm
ISBN:	9783110447422 3110447428

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MARC


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Record in the Search Index

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adam_text	CONTENTS PREFACE * VII PART I: THEORY CHAPTER 1 FIRST-ORDER DIFFERENTIAL EQUATIONS * 3 1.1 PRELIMINARIES * 3 1.2 CLASSES OF FIRST-ORDER DIFFERENTIAL EQUATIONS * 6 1.2.1 DIFFERENTIAL EQUATIONS WITH SEPARABLE VARIABLES * 6 1.2.2 DIFFERENTIAL EQUATIONS OF HOMOGENEOUS TYPE * 7 1.2.3 FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS * 8 1.2.4 BERNOULLI EQUATIONS * 13 1.2.5 RICCATI EQUATIONS * 14 1.3 MATHEMATICAL MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS * 1.3.1 RADIOACTIVE DECAY * 15 1.3.2 NEWTONS LAW OF HEAT TRANSFER ----- 16 1.3.3 CHEMICAL REACTIONS 17 1.3.4 POPULATION GROWTH OF A SINGLE SPECIES * 18 1.3.5 THE GOMPERTZ EQUATION ----- 20 CHAPTER 2 LINEAR DIFFERENTIAL SYSTEMS * 22 2.1 PRELIMINARIES * 22 2.2 MATHEMATICAL MODELING WITH LINEAR DIFFERENTIAL SYSTEMS * 23 2.3 MATRIX NOTATION FOR SYSTEMS * 26 2.4 SUPERPOSITION PRINCIPLE FOR LINEAR SYSTEMS * 27 2.5 LINEAR DIFFERENTIAL SYSTEMS WITH CONSTANT COEFFICIENTS * 28 2.5.1 THE GENERAL SOLUTION ----- 28 2.5.2 STRUCTURE OF SOLUTION SET FOR HOMOGENEOUS LINEAR SYSTEMS * 31 2.5.3 THE CONCEPT OF FUNDAMENTAL MATRIX * 32 2.5.4 METHOD OF EIGENVALUES AND EIGENVECTORS * 35 2.6 METHOD OF VARIATION OF PARAMETERS * 40 2.7 HIGHER-DIMENSIONAL LINEAR SYSTEMS * 42 2.8 USE OF THE JORDAN CANONICAL FORM OF A MATRIX * 44 2.9 DYNAMIC ASPECTS OF DIFFERENTIAL SYSTEMS * 46 2.10 PRELIMINARIES OF STABILITY * 52 CHAPTER 3 SECOND-ORDER DIFFERENTIAL EQUATIONS * 53 3.1 NEWTONS SECOND LAW OF MOTION ----- 53 3.2 REDUCTION OF ORDER ----- 54 3.3 EQUIVALENCE TO A FIRST-ORDER SYSTEM 57 3.4 THE METHOD OF ELIMINATION ----- 58 3.5 LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS * 59 3.5.1 THE SOLUTION SET ----- 59 3.5.2 HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS * 59 3.5.3 VARIATION OF PARAMETERS METHOD * 61 3.5.4 THE METHOD OF UNDETERMINED COEFFICIENTS * 62 3.5.5 EULER EQUATIONS * 64 3.6 BOUNDARY VALUE PROBLEMS * 66 3.7 HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS * 69 CHAPTER 4 NONLINEAR DIFFERENTIAL EQUATIONS * 72 4.1 MATHEMATICAL MODELS EXPRESSED BY NONLINEAR SYSTEMS * 72 4.1.1 THE LOTKA-VOLTERRA MODEL ----- 72 4.1.2 THE SIR EPIDEMIC MODEL ----- 73 4.1.3 AN IMMUNOLOGICAL MODEL * 74 4.1.4 A MODEL IN HEMATOLOGY * 75 4.2 GRONWATLS INEQUALITY 75 4.3 UNIQUENESS OF SOLUTIONS FOR THE CAUCHY PROBLEM * 77 4.4 CONTINUOUS DEPENDENCE OF SOLUTIONS ON THE INITIAL VALUES * 81 4.5 THE CAUCHY PROBLEM FOR SYSTEMS * 83 4.6 THE CAUCHY PROBLEM FOR HIGHER-ORDER EQUATIONS * 84 4.7 PERIODIC SOLUTIONS * 85 4.8 PICARDS METHOD OF SUCCESSIVE APPROXIMATIONS 88 4.8.1 PICARDS ITERATION 88 4.8.2 THE INTERVAL OF PICARDS ITERATION 91 4.8.3 CONVERGENCE OF PICARDS ITERATION 92 4.9 EXISTENCE OF SOLUTIONS FOR THE CAUCHY PROBLEM * 93 CHAPTER 5 STABILITY OF SOLUTIONS * 97 5.1 THE NOTION OF A STABLE SOLUTION * 97 5.2 STABILITY OF LINEAR SYSTEMS * 99 5.3 STABILITY OF LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS * 100 5.4 STABILITY OF SOLUTIONS OF NONLINEAR SYSTEMS * 101 5.5 METHOD OF LYAPUNOV FUNCTIONS * 106 5.6 GLOBALLY ASYMPTOTICALLY STABLE SYSTEMS * 111 CHAPTER 6 DIFFERENTIAL SYSTEMS WITH CONTROL PARAMETERS * 113 6.1 BIFURCATIONS * 113 6.2 HOPF BIFURCATIONS ----- 115 6.3 OPTIMIZATION OF DIFFERENTIAL SYSTEMS * 119 6.4 DYNAMIC OPTIMIZATION OF DIFFERENTIAL SYSTEMS * 122 PART II: EXERCISES SEMINAR 1 1.1 1.2 1.3 1.4 CLASSES OF FIRST-ORDER DIFFERENTIAL EQUATIONS * 127 SOLVED EXERCISES * 127 PROPOSED EXERCISES * 129 SOLUTIONS * 130 PROJECT: PROBLEMS OF GEOMETRY THAT LEAD TO DIFFERENTIAL EQUATIONS * 131 SEMINAR 2 2.1 2.2 2.3 2.4 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS * 133 SOLVED EXERCISES * 133 PROPOSED EXERCISES * 135 HINTS AND ANSWERS * 136 PROJECT: INFLUENCE OF EXTERNAL ACTIONS OVER THE EVOLUTION OF SOME PROCESSES * 136 SEMINAR 3 3.1 3.2 3.3 3.4 LINEAR DIFFERENTIAL SYSTEMS * 139 SOLVED EXERCISES * 139 PROPOSED EXERCISES * 143 HINTS AND SOLUTIONS * 145 PROJECT: MATHEMATICAL MODELS REPRESENTED BY LINEAR DIFFERENTIAL SYSTEMS * 146 SEMINAR 4 4.1 4.2 4.3 4.4 SECOND-ORDER DIFFERENTIAL EQUATIONS * 148 SOLVED EXERCISES * 148 PROPOSED EXERCISES * 150 SOLUTIONS * 151 PROJECT: BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS ----- 152 SEMINAR 5 5.1 5.2 5.3 5.4 CORNWALL S INEQUALITY * 154 SOLVED EXERCISES * 154 PROPOSED EXERCISES * 157 HINTS AND SOLUTIONS * 157 PROJECT: INTEGRAL AND DIFFERENTIAL INEQUALITIES * 158 SEMINAR 6 METHOD OF SUCCESSIVE APPROXIMATIONS * 163 6.1 6.2 SOLVED EXERCISES * 163 PROPOSED EXERCISES * 164 6.3 HINTS AND SOLUTIONS * 165 6.4 PROJECT: THE VECTORIAL METHOD FOR THE TREATMENT OF NONLINEAR DIFFERENTIAL SYSTEMS * 165 SEMINAR 7 STABILITY OF SOLUTIONS * 170 7.1 SOLVED EXERCISES * 170 7.2 PROPOSED EXERCISES * 172 7.3 HINTS AND SOLUTIONS * 173 7.4 PROJECT: STABLE AND UNSTABLE INVARIANT MANIFOLDS * 173 PART III: MAPLE CODE LAB 1 INTRODUCTION TO MAPLE * 179 1.1 NUMERICAL CALCULUS * 179 1.2 SYMBOLIC CALCULUS * 181 LAB 2 DIFFERENTIAL EQUATIONS WITH MAPLE * 185 2.1 THE DETOOLS PACKAGE * 185 2.2 WORKING THEMES ----- 186 LAB 3 LINEAR DIFFERENTIAL SYSTEMS * 188 3.1 THE LINALG PACKAGE * 188 3.2 LINEAR DIFFERENTIAL SYSTEMS * 188 3.3 WORKING THEMES * 190 LAB 4 SECOND-ORDER DIFFERENTIAL EQUATIONS * 191 4.1 SPRING-MASS OSCILLATOR EQUATION WITH MAPLE * 191 4.2 BOUNDARY VALUE PROBLEMS WITH MAPLE * 193 4.3 WORKING THEMES ----- 193 LAB 5 NONLINEAR DIFFERENTIAL SYSTEMS * 195 5.1 THE LOTKA-VOLTERRA SYSTEM * 195 5.2 A MODEL FROM HEMATOLOGY * 196 5.3 WORKING THEMES * 197 LAB 6 NUMERICAL COMPUTATION OF SOLUTIONS * 198 6.1 INITIAL VALUE PROBLEMS * 198 6.2 BOUNDARY VALUE PROBLEMS * 199 6.3 WORKING THEMES * 202 LAB 7 WRITING CUSTOM MAPLE PROGRAMS * 204 7.1 METHOD OF SUCCESSIVE APPROXIMATIONS * 204 7.2 EULERS METHOD ----- 206 7.3 THE SHOOTING METHOD------208 7.4 WORKING THEMES 211 LAB 8 DIFFERENTIAL SYSTEMS WITH CONTROL PARAMETERS * 212 8.1 BIFURCATIONS * 212 8.2 OPTIMIZATION WITH MAPLE------213 8.3 WORKING THEMES ----- 215 BIBLIOGRAPHY * 217 INDEX * 219
any_adam_object	1
author	Precup, Radu 1955-
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ctrlnum	(OCoLC)1024117672 (DE-599)DNB1078861226
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	510 - Mathematics
dewey-raw	510
dewey-search	510
dewey-sort	3510
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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spelling	Precup, Radu 1955- Verfasser (DE-588)1028201435 aut Ordinary differential equations example-driven, including Maple Code Radu Precup Berlin ; Boston De Gruyter [2018] © 2018 XIII, 221 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Maple Programm (DE-588)4209397-1 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Fachhochschul-/Hochschulausbildung Algorithmus (DE-588)4001183-5 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Maple Programm (DE-588)4209397-1 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-044744-6 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-044750-7 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110447422&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030130376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Precup, Radu 1955- Ordinary differential equations example-driven, including Maple Code Maple Programm (DE-588)4209397-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Algorithmus (DE-588)4001183-5 gnd
subject_GND	(DE-588)4209397-1 (DE-588)4020929-5 (DE-588)4001183-5
title	Ordinary differential equations example-driven, including Maple Code
title_auth	Ordinary differential equations example-driven, including Maple Code
title_exact_search	Ordinary differential equations example-driven, including Maple Code
title_full	Ordinary differential equations example-driven, including Maple Code Radu Precup
title_fullStr	Ordinary differential equations example-driven, including Maple Code Radu Precup
title_full_unstemmed	Ordinary differential equations example-driven, including Maple Code Radu Precup
title_short	Ordinary differential equations
title_sort	ordinary differential equations example driven including maple code
title_sub	example-driven, including Maple Code
topic	Maple Programm (DE-588)4209397-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Algorithmus (DE-588)4001183-5 gnd
topic_facet	Maple Programm Gewöhnliche Differentialgleichung Algorithmus
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