Introduction to differential equations with applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Harper & Row
1986
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung graph. Darst. |
| ISBN: | 0060409428 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to differential equations with applications |c Fred Brauer and John A. Nohel |
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Record in the Search Index
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| adam_text | Titel: Introduction to differential equations with applications
Autor: Brauer, Fred
Jahr: 1986
Contents Preface ix CHAPTER 1 INTRODUCTION TO FIRST-ORDER DIFFERENTIAL EQUATIONS 1 1.1 Some Population Growth Problems 1 1.2 Equations with Variables Separable 6 1.3 Some Applications of Separable Equations 17 1.4 Linear Equations of First Order 27 1.5 Some Applications of First-Order Linear Equations 35 • 1.6 Existence and Uniqueness for First-Order Equations 46 1.7 Direction Fields 59 • 1.8 Equilibrium Points for First-Order Equations 65 • 1.9 Numerical Approximation of Solutions of First-Order Equations 73 CHAPTER 2 SOLUTIONS OF SOME SECOND-ORDER DIFFERENTIAL EQUATIONS 88 2.1 The Mass-Spring System 88 2.2 Solutions of the Linear Differential Equation y + o) 2 y=0 95 2.3 Solution of Linear Homogeneous Differential Equations of Second Order with Constant Coefficients 101 2.4 Linearity and Some of Its Consequences 112 2.5 Linear Nonhomogeneous Second-Order Differential Equations 114 2.6 Some Applications of Linear Second-Order Differential Equations 127 2.7 Some Linear and Nonlinear Second-Order Equations Solvable by First-Order Methods 145 • 2.8 Numerical Approximation of Solutions of Second-Order Equations 153 •Denotes optional material.
vi CONTENTS CHAPTER 3 LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS AND LINEAR DIFFERENTIAL EQUATIONS OF ARBITRARY ORDER 165 3.1 Introduction to Linear Systems 166 3.2 Solutions of Some Linear Systems with Constant Coefficients 175 3.3 Vector-Matrix Notation for Linear Systems 180 3.4 Linear Homogeneous Systems 187 3.5 Linear Homogeneous Systems of Differential Equations with Constant Coefficients 199 3.6 Linear Systems with Constant Coefficients: Multiple Eigenvalues 211 3.7 Linear Nonhomogeneous Systems 224 3.8 Linear Differential Equations of Order n 230 3.9 The Euler Equation 245 CHAPTER 4 THE LAPLACE TRANSFORM 255 4.1 Definition and Properties of Laplace Transforms 255 4.2 The Inverse Transform 271 4.3 Applications to Linear Differential Equations with Constant Coefficients 279 4.4 An Application to Electric Circuits and Impulses 286 4.5 Applications to Linear Systems of Differential Equations 294 4.6 A Table of Laplace Transforms 304 CHAPTER 5 SERIES SOLUTIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH APPLICATIONS 306 5.1 Review of the Properties of Power Series 306 5.2 An Example 310 5.3 Power-series Solutions About an Ordinary Point 314 5.4 Singular Points of Linear Differential Equations 322 5.5 Three Examples of Solutions About a Regular Singular Point 326 5.6 Solutions About a Regular Singular Point: The Method of Frobenuis 334 5.7 Solutions About a Regular Singular Point: Exceptional Cases 344 5.8 Singularities at Infinity 357 5.9 Properties of Bessel Functions 361 5.10 Some Properties of Legendre Polynomials 378 CHAPTER 6 AN INTRODUCTION TO THE QUALITATIVE STUDY OF DIFFERENTIAL EQUATIONS 383 6.1 Existence of Solutions 384 6.2 Uniqueness of Solutions 399 6.3 Existence Theory for Second-Order Equations 404 6.4 Equilibrium Points, the Phase Plane, and Linearization 410 6.5 Phase Plane Analysis of Real Autonomous Second-Order Equations 417 6.6 Nonlinear Systems with One Degree of Freedom 432
CONTENTS vii CHAPTER 7 AN INTRODUCTION TO THE WAVE EQUATIONS, SEPARATION OF VARIABLES, AND FOURIER SERIES 444 7.1 Formulation of Boundary-Initial- Value Problems for the One-Dimensional Wave Equation 444 7.2 Separation of Variables in Boundary-Initial Value Problems for the Wave Equation 453 7.3 Fourier Series Expansions 465 7.4 Solution of Boundary-Initial-Value Problems for the Wave Equation 478 • 7.5 Some Properties of Solutions of the Wave Equation 486 • 7.6 The Wave Equation in More Than One Space Dimension 499 CHAPTER 8 THE HEAT AND LAPLACE EQUATIONS 510 8.1 Heat Flow in a Plate and in a Rod 510 8.2 Solution of Heat Flow Problems by Separation of Variables 521 8.3 Solution of the Laplace Equation by Separation of Variables 531 • 8.4 Some Properties of Solutions of the Laplace Equation 546 • 8.5 Some Properties of Solutions of the Heat Equation 559 • 8.6 Properly Posed Problems 567 APPENDIX 1 DETERMINANTS AND LINEAR SYSTEMS A-1 APPENDIX 2 COMPLEX NUMBERS AND COMPLEX-VALUED FUNCTIONS A-4 APPENDIX 3 POLYNOMIAL EQUATIONS A-7 APPENDIX 4 IMPROPER AND INFINITE INTEGRALS, DIFFERENTIATION OF INTEGRALS A-9 APPENDIX 5 SOME PROPERTIES OF THE GAMMA FUNCTION A-12 APPENDIX 6 ANSWERS TO ODD-NUMBERED EXERCISES A-15 INDEX 1-1
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:40Z |
| institution | BVB |
| isbn | 0060409428 |
| language | English |
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| physical | Getr. Zählung graph. Darst. |
| publishDate | 1986 |
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| publisher | Harper & Row |
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| spelling | Brauer, Fred 1932- Verfasser (DE-588)12370085X aut Introduction to differential equations with applications Fred Brauer and John A. Nohel New York u.a. Harper & Row 1986 Getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 Nohel, John A. 1924- Verfasser (DE-588)118120921 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brauer, Fred 1932- Nohel, John A. 1924- Introduction to differential equations with applications Differential equations Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Introduction to differential equations with applications |
| title_auth | Introduction to differential equations with applications |
| title_exact_search | Introduction to differential equations with applications |
| title_full | Introduction to differential equations with applications Fred Brauer and John A. Nohel |
| title_fullStr | Introduction to differential equations with applications Fred Brauer and John A. Nohel |
| title_full_unstemmed | Introduction to differential equations with applications Fred Brauer and John A. Nohel |
| title_short | Introduction to differential equations with applications |
| title_sort | introduction to differential equations with applications |
| topic | Differential equations Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differential equations Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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