|
Showing 1 - 4 of
4 matches in All Departments
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.
This book is designed as a text for a first-year graduate algebra
course. As necessary background we would consider a good
undergraduate linear algebra course. An undergraduate abstract
algebra course, while helpful, is not necessary (and so an
adventurous undergraduate might learn some algebra from this book).
Perhaps the principal distinguishing feature of this book is its
point of view. Many textbooks tend to be encyclopedic. We have
tried to write one that is thematic, with a consistent point of
view. The theme, as indicated by our title, is that of modules
(though our intention has not been to write a textbook purely on
module theory). We begin with some group and ring theory, to set
the stage, and then, in the heart of the book, develop module
theory. Having developed it, we present some of its applications:
canonical forms for linear transformations, bilinear forms, and
group representations. Why modules? The answer is that they are a
basic unifying concept in mathematics. The reader is probably
already familiar with the basic role that vector spaces play in
mathematics, and modules are a generaliza tion of vector spaces.
(To be precise, modules are to rings as vector spaces are to
fields."
This book is designed as a text for a first-year graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely generated modules over a principal ideal domain. They then treat canonical form theory in linear algebra as an application of this fundamental theorem. Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and modules and apply these results in the final chapter to study group represetations by viewing a representation of a group G over a field F as an F(G)-module. The book emphasizes proofs with a maximum of insight and a minimum of computation in order to promote understanding. However, extensive material on computation (for example, computation of canonical forms) is provided.
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.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Tenet
John David Washington, Robert Pattinson, …
DVD
R53
Discovery Miles 530
|