Course In Analysis, A - Vol. Ii: Differentiation And

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Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus

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 Stoneâ€“Weierstrass theorem or the Arzelaâ€“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 (â€“Darbouxâ€“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.
Country USA
Brand Scientific Publishing
Manufacturer Wspc
Binding Paperback
ReleaseDate 2016-06-29
UnitCount 1
Format Illustrated
EANs 9789813140967

Country	USA
Brand	Scientific Publishing
Manufacturer	Wspc
Binding	Paperback
ReleaseDate	2016-06-29
UnitCount	1
Format	Illustrated
EANs	9789813140967

Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus

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