2
Course In Analysis, A - Vol. Ii
(Paperback)

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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.

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.

AuthorKristian P. Evans
BindingPaperback
EAN9789813140967
FormatImport
ISBN9813140968
Height957 mm
Length650 mm
Width178 mm
LanguageEnglish
Language TypePublished
Number Of Pages788
Package Quantity1
Product GroupBook
Publication Date2016-06-30
PublisherWorld Scientific Publishing Co Pte Ltd
StudioWorld Scientific Publishing Co Pte Ltd
Sales Rank500301

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General information about 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus
  • The author associated with 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is Kristian P. Evans.
  • The EAN for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 9789813140967.
  • The format for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is Import.
  • The ISBN for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 9813140968.
  • The height for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 957 mm.
  • The length for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 650 mm.
  • The width for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 178 mm.
  • The language for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is English.
  • The binding of 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is Paperback.
  • The number of pages for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus are 788.
  • The quantity for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus in a package is 1.
  • 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is grouped in Book group of products.
  • The publication date for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 2016-06-30.
  • The publisher for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is World Scientific Publishing Co Pte Ltd.
  • The producer for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is World Scientific Publishing Co Pte Ltd.
  • The sales rank for 2: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus is 500301.