Ordinary Differential Equations (undergraduate Texts In Mathematics)
by William A. Adkins /
2012 / English / PDF
4.7 MB Download
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.
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.
