Ordinary Differential Equations

Mark G. Davidson

ISBN 10: 1489987673 / ISBN 13: 9781489987679

Published by Springer New York, Springer US Jun 2015, 2015

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 816 pp. Englisch.

Seller Inventory # 9781489987679

Bibliographic Details

• Title: Ordinary Differential Equations
• Publisher: Springer New York, Springer US Jun 2015
• Publication Date: 2015
• Language: English
• ISBN 10: 1489987673
• ISBN 13: 9781489987679
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.

About the Author

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