A course in multivariable calculus and analysis

The Resource A course in multivariable calculus and analysis
Label
A course in multivariable calculus and analysis
Statement of responsibility
Sudhir R. Ghorpade, Balmohan V. Limaye
Creator
Contributor
Subject
Genre
Language
eng
Summary
This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments'' indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus
Member of
Cataloging source
GW5XE
Dewey number
515.94
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA303.2
LC item number
.G56 2010
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Undergraduate texts in mathematics,
Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Missouri Libraries. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...