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.

Rese�a del editor:

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.

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.

Anbieterinformationen

Hello! Ria Christie Collections is an online venture that was initially set up in 2012 to sell books. We do not have a physical high street store. We are professional online booksellers. We only sell brand new books in perfect condition that we source from various suppliers and the publishers. Primarily, our aim is to provide an excellent service to all our customers. We always work as a team to achieve this. Our other objectives are to: 1. Ensure that all our products reach their destination quickly in a safe and secure manner 2. Answer to all our customer queries within 24 hours 3. Ensure that our customers are happy with their purchases 4. Provide all the items at a competitive price 5. Always listen to our customers Ria Christie Collections is not a registered company. It is a Sole Trader venture. Other key information is shown below: Contact Person Name: Rakesh Luchmun (Mr) Storefront Name: Ria Christie Collections Place of Establishment Address: Suite B; ARUN House; ARUN Building Arundel Road Uxbridge UB8 2RR United Kingdom E-Mail Address: riachristie@hotmail.co.uk VAT Number: GB 160 5650 25 We always work hard and aim to comply with all of Abebooks Policies. If you have any issues, please do not hesitate to write to us whether before or after a purchase. We promise to reply to you promptly and, in any case, within 24 hours. Thank you kindly! Yours sincerely Mr Rakesh Luchmun (Founder) and the Ria Christie Collections Team

Zur Homepage des Verk�ufers

Unternehmensdaten des Verk�ufers

Ryefield Investments Limited
175 Pield Heath Road, Uxbridge, UB8 3NL, United Kingdom

Gesch�ftsbedingungen:

All Returns and Refund are as per Abebooks policies.

Versandinformationen:

Orders usually ship within 2 business days. If your book order is heavy or oversized, we may contact you to let you know extra shipping is required. Thank you!

Zahlungsarten
akzeptiert von diesem Verk�ufer

Zu Kaufgesuchen hinzuf�gen

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

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

Jacob, Niels

Neu - Softcover

Unternehmensdaten des Verk�ufers