Name: Course in Analysis, a - Vol. Ii: Differentiation and Integration of Functions of Several Variables, Vector Calculus: Volume 2 (en Inglés)
Price: 1935.16 MXN
Availability: InStock
Author: Kristian P. Evans; Niels Jacob
ISBN: 9789813140967

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portada Course in Analysis, a - Vol. Ii: Differentiation and Integration of Functions of Several Variables, Vector Calculus: Volume 2 (en Inglés)

Formato

Libro Físico

Editorial

World Scientific Publishing Co Pte Ltd

Autor

Kristian P. Evans; Niels Jacob

Año

2016

Idioma

Inglés

N° páginas

788

Encuadernación

Tapa Blanda

ISBN13

9789813140967

N° edición

Categorías

Cálculo

Course in Analysis, a - Vol. Ii: Differentiation and Integration of Functions of Several Variables, Vector Calculus: Volume 2 (en Inglés)

Kristian P. Evans; Niels Jacob (Autor) · World Scientific Publishing Co Pte Ltd · Tapa Blanda

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Reseña del libro "Course in Analysis, a - Vol. Ii: Differentiation and Integration of Functions of Several Variables, Vector Calculus: Volume 2 (en Inglés)"

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.