Ordinary Differential Equations | Buch

Cover: 9781461436171 | Ordinary Differential Equations | Mark G. Davidson (u. a.) | Buch

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Sprache: Englisch

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Beschreibung

Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations.
Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.

Über den Autor

William A. Adkins and Mark G. Davidson are currently professors of mathematics at Louisiana State University.

Zusammenfassung

Contains numerous helpful examples and exercises that provide motivation for the reader

Presents the Laplace transform early in the text and uses it to motivate and develop solution methods for differential equations

Takes a streamlined approach to linear systems of differential equations

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Inhaltsverzeichnis

Preface.- 1 First Order Differential Equations.- 2 The Laplace Transform.- 3 Second Order Constant Coefficient Linear Differential Equations.- 4 Linear Constant Coefficient Differential Equations.- 5 Second Order Linear Differential Equations.- 6 Discontinuous Functions and the Laplace Transform.- 7 Power Series Methods.- 8 Matrices .- 9 Linear Systems of Differential Equations.- A Appendix.- B Selected Answers.- C Tables.- Symbol Index.- Index.

Details

Erscheinungsjahr:	2012
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xiii 799 S. 121 s/w Illustr. 799 p. 121 illus.
ISBN-13:	9781461436171
ISBN-10:	1461436176
Sprache:	Englisch
Herstellernummer:	10986721
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Davidson, Mark G. Adkins, William A.
Hersteller:	Springer New York Springer US, New York, N.Y. Undergraduate Texts in Mathematics
Maße:	241 x 160 x 49 mm
Von/Mit:	Mark G. Davidson (u. a.)
Erscheinungsdatum:	01.07.2012
Gewicht:	1,373 kg

Artikel-ID: 106448892