Ordinary differential equations a first course

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Bibliographische Detailangaben
Hauptverfasser: Brauer, Fred 1932- (VerfasserIn), Nohel, John A. 1924- (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Menlo Park, Calif. u.a. Benjamin 1973
Ausgabe:2. ed.
Schriftenreihe:University mathematics series
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Datensatz im Suchindex

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adam_text Contents Chapter 1 Introduction to First Order Differential Equations 1.1 Some population and closely related growth problems 1 1.2 First order equations 5 1.3 Equations with variables separable 9 1.4 Linear equations of the first order 20 1.5 Direction fields 28 1.6 Existence and uniqueness for first order equations 30 Chapter 2 Introduction to Second Order Differential Equations 2.1 The mass spring system 38 2.2 The pendulum problem 43 2.3 Further examples of motion problems 48 2.4 Second order equations solvable by first order methods 49 2.5 The existence and uniqueness theorems for second and higher order equa¬ tions 60 Chapter 3 Linear Differential Equations 3.1 Introduction 65 3.2 Linearity 68 3.3 Linear homogeneous equations 70 3.4 Solution of linear homogeneous differential equations of second order with constant coefficients 83 3.5 Linear homogeneous equations of arbitrary order with constant co¬ efficients 93 3.6 Reduction of order 95 3.7 Linear nonhomogeneous equations 99 3.8 Resonance 111 Chapter 4 Linear System of Differential Equations 4.1 Introduction 114 vii viii Contents 4.2 The existence and uniqueness theorem 130 4.3 Linear homogeneous systems 134 4.4 Linear nonhomogeneous systems 147 4.5 Nonlinear system of first order equations 156 Chapter 5 Eigenvalues, Eigenvectors, and Linear Systems with Constant Coefficients 5.1 The exponential of a matrix 165 5.2 Eigenvalues and eigenvectors of matrices 169 5.3 Calculation of a fundamental matrix 174 5.4 Two dimensional linear systems 180 5.5 Some population problems 192 5.6 The general case 197 5.7 Solution of Example 9, Section 4.2: An electric circuit 206 Chapter 6 Series Solutions of Linear Differential Equations 6.1 Introduction 212 6.2 Review of properties of power series 214 6.3 Second order linear equations with analytic coefficients 217 6.4 Proof of theorem on solutions in power series 223 6.5 Singular points of linear differential equations 228 6.6 Solutions about a regular singular point: Examples 232 6.7 Solutions about a regular singular point: Theorem 239 6.8 Solutions about regular singular point: Exceptional cases 244 6.9 The Bessel equation and some properties of Bessel functions 253 6.10 Singularities at infinity 263 6.11 Irregular singular points, with an introduction to asymptotic expansions 266 Chapter 7 Boundary Value Problems 7.1 Introduction 278 7.2 Examples of homogeneous boundary value problems 281 7.3 Examples of nonhomogeneous boundary value problems The Green s function 288 7.4 Self adjoint boundary value problems for the operator L(y)= —y 293 7.5 Sturm Liouville problems 298 7.6 Remarks on a singular boundary value problem 303 7.7 Nonhomogeneous boundary value problems and Green s function 306 Chapter 8 Existence Theory 8.1 Existence of solutions 314 8.2 Uniqueness of solutions 329 8.3 Continuation of solutions 333 8.4 The nonlinear simple pendulum 340 8.5 Existence theory for systems of first order equations and higher order equations 346 8.6 Linear systems 349 8.7 Dependence on initial conditions 353 Contents ix Chapter 9 Numerical Methods of Solution 9.1 The Euler method 357 9.2 The modified Euler method 368 9.3 The Milne method 372 9.4 Stability, consistency, and convergence 381 9.5 Runge kutta methods 385 9.6 Numerical methods for systems and equations of higher order 389 Chapter 10 The Laplace Transform 10.1 Introduction 392 10.2 Basic properties of the Laplace transform 393 10.3 The inverse transform 401 10.4 Applications to linear equations with constant coefficients 406 10.5 Applications to linear systems 415 10.6 A table of Laplace transforms 422 Appendix 1 Determinants and Linear Systems 424 Appendix 2 Polynomial Equations 427 Appendix 3 Complex Numbers and Complex Valued Functions 429 Appendix 4 The Exponential Matrix 433 Appendix 5 Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of Matrices 436 Bibliography 449 Answers to Selected Exercises 450 Index 465
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author Brauer, Fred 1932-
Nohel, John A. 1924-
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indexdate 2024-12-23T12:45:54Z
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physical IX, 470 S. graph. Darst.
publishDate 1973
publishDateSearch 1973
publishDateSort 1973
publisher Benjamin
record_format marc
series2 University mathematics series
spellingShingle Brauer, Fred 1932-
Nohel, John A. 1924-
Ordinary differential equations a first course
Differential equations
Differentialgleichung (DE-588)4012249-9 gnd
Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd
subject_GND (DE-588)4012249-9
(DE-588)4020929-5
title Ordinary differential equations a first course
title_auth Ordinary differential equations a first course
title_exact_search Ordinary differential equations a first course
title_full Ordinary differential equations a first course Fred Brauer ; John A. Nohel
title_fullStr Ordinary differential equations a first course Fred Brauer ; John A. Nohel
title_full_unstemmed Ordinary differential equations a first course Fred Brauer ; John A. Nohel
title_short Ordinary differential equations
title_sort ordinary differential equations a first course
title_sub a first course
topic Differential equations
Differentialgleichung (DE-588)4012249-9 gnd
Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd
topic_facet Differential equations
Differentialgleichung
Gewöhnliche Differentialgleichung
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005578171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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