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

Jacob, Niels

 
9789813140967: Course In Analysis, A - Vol. Ii: Differentiation And Integration Of Functions Of Several Variables, Vector Calculus
Couverture souple
ISBN 10 : 9813140968 ISBN 13 : 9789813140967
Editeur : Wspc, 2016

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Wspc
Date d'édition
2016
Langue
anglais
ISBN 10 
9813140968
ISBN 13 
9789813140967
Reliure
Broché
Nombre de pages
788
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9789813140950: A Course in Analysis: Differentiation and Integration of Functions of Several Variables, Vector Calculus

Edition présentée

ISBN 10 :  981314095X ISBN 13 :  9789813140950
Editeur : World Scientific Publishing Co P..., 2016
Couverture rigide