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Note publique d'information : 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
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