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＜電子ブック＞
Ordinary Differential Equations / by William A. Adkins, Mark G. Davidson
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2012.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2012
大きさ	XIII, 799 p. 121 illus : online resource
著者標目	*Adkins, William A author Davidson, Mark G author SpringerLink (Online service)
件　名	LCSH:Differential equations FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4614-3618-8

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