Multidimensional Real Analysis I
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Author | : J. J. Duistermaat |
Publisher | : Cambridge University Press |
Total Pages | : 444 |
Release | : 2004-05-06 |
Genre | : Mathematics |
ISBN | : 1139451197 |
Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2004 |
Genre | : Functions of real variables |
ISBN | : |
Author | : Johannes Jisse Duistermaat |
Publisher | : Cambridge Studies in Advanced Mathematics |
Total Pages | : 798 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780521829304 |
Two-volume set of the authors' comprehensive and innovative work on multidimensional real analysis.
Author | : J. J. Duistermaat |
Publisher | : Cambridge University Press |
Total Pages | : 398 |
Release | : 2004-05-06 |
Genre | : Mathematics |
ISBN | : 1139451871 |
Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Author | : Richard Wheeden |
Publisher | : CRC Press |
Total Pages | : 289 |
Release | : 1977-11-01 |
Genre | : Mathematics |
ISBN | : 1482229536 |
This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Author | : Johannes Jisse Duistermaat |
Publisher | : |
Total Pages | : 798 |
Release | : 2004 |
Genre | : Functions of real variables |
ISBN | : 9787510005183 |
Author | : George W. Hart |
Publisher | : Springer Science & Business Media |
Total Pages | : 242 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242088 |
This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.
Author | : N. L. Carothers |
Publisher | : Cambridge University Press |
Total Pages | : 420 |
Release | : 2000-08-15 |
Genre | : Mathematics |
ISBN | : 9780521497565 |
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Author | : Marshall Evans Munroe |
Publisher | : Courier Dover Publications |
Total Pages | : 401 |
Release | : 2019-05-15 |
Genre | : Mathematics |
ISBN | : 0486840069 |
A second-year calculus text, this volume is devoted primarily to topics in multidimensional analysis. Concepts and methods are emphasized, and rigorous proofs are sometimes replaced by relevant discussion and explanation. Because of the author's conviction that the differential provides a most elegant and useful tool, especially in a multidimensional setting, the notion of the differential is used extensively and matrix methods are stressed in the study of linear transformations. The first three chapters offer introductory material on functions and variables, differentials, and vectors in the plane. Succeeding chapters examine topics in linear algebra, partial derivatives, and applications as well as topics in vector differential calculus. The final chapters explore multiple integrals in addition to line and surface integrals. Exercises appear throughout the text, and answers are provided, making the book ideal for self-study.
Author | : Charles Chapman Pugh |
Publisher | : Springer Science & Business Media |
Total Pages | : 445 |
Release | : 2013-03-19 |
Genre | : Mathematics |
ISBN | : 0387216847 |
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.