9789813140950-981314095X-A Course in Analysis: Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus

A Course in Analysis: Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus

ISBN-13: 9789813140950
ISBN-10: 981314095X
Edition: Illustrated
Author: Niels Jacob, Kristian P Evans
Publication date: 2016
Publisher: World Scientific Publishing Co
Format: Hardcover 788 pages
FREE shipping on ALL orders

Book details

ISBN-13: 9789813140950
ISBN-10: 981314095X
Edition: Illustrated
Author: Niels Jacob, Kristian P Evans
Publication date: 2016
Publisher: World Scientific Publishing Co
Format: Hardcover 788 pages

Summary

Acknowledged authors Niels Jacob, Kristian P Evans wrote A Course in Analysis: Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus comprising 788 pages back in 2016. Textbook and eTextbook are published under ISBN 981314095X and 9789813140950. Since then A Course in Analysis: Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as the continuity of mappings. This is followed by introducing partial derivatives of real-valued functions and the differential of mappings. Many chapters deal with applications, in particular to geometry (parametric curves and surfaces, convexity), but topics such as extreme values and Lagrange multipliers, or curvilinear coordinates are considered too. On the more abstract side results such as the Stone Weierstrass theorem or the Arzela-Ascoli theorem are proved in detail. The first part ends with a rigorous treatment of line integrals.

The second part handles iterated and volume integrals for real-valued functions. Here we develop the Riemann (-Darboux-Jordan) theory. A whole chapter is devoted to boundaries and Jordan measurability of domains. We also handle in detail improper integrals and give some of their applications.

The final part of this volume takes up a first discussion of vector calculus. Here we present a working mathematician's version of Green's, Gauss' and Stokes' theorem. Again some emphasis is given to applications, for example to the study of partial differential equations. At the same time we prepare the student to understand why these theorems and related objects such as surface integrals demand a much more advanced theory which we will develop in later volumes.

This volume offers more than 260 problems solved in complete detail which should be of great benefit to every serious student.

Readership: Undergraduate students in mathematics.

Rate this book Rate this book

We would LOVE it if you could help us and other readers by reviewing the book