Ordinary Differential Equations

ISBN-13: 9781489987679 / Angielski / Miękka / 2015 / 799 str.

William Adkins; Mark G. Davidson

Opis

Unlike other texts on differential equations, this one provides an early presentation of the Laplace transform before deploying it in the motivation and development of many of the differential equation concepts for which it is particularly well suited.

Recenzje

From the reviews:

"The book is meant for an introductory course for second-year undergraduates whose interest in the theory of differential equations is greater than that of the group of students normally taking the class. ... Adkins and Davidson ... explain the theory in more detail, and they discuss both the geometric and algebraic meaning of theorems. ... The volume includes two optional subjects, power series and matrices, in separate chapters. Summing Up: Recommended. Lower-division undergraduates." (M. Bona, Choice, Vol. 50 (5), January, 2013)

"This volume is ideally suited to any standard undergraduate course in ordinary differential equations at all levels for mathematics and engineering students. ... This book is clearly written, contains many illustrations and is very useful for students and teachers. This text is a welcome addition to the differential equations literature, and is strongly recommended as a textbook for classroom use or for individual study." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1259, 2013)

Spis treści

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.

O autorze

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

Blurb

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.