A Course in Analysis Volume 2 Differentiation and Integration of Functions of Several Variables Vector Calculus

e use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More × A Course in Analysis cover A Course in Analysis Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus https://doi.org/10.1142/10059 | August 2016 Pages: 788 By (author): Niels Jacob (Swansea University, UK) and Kristian P Evans (Swansea University, UK) Tools Share Save for later ISBN: 978-981-3140-95-0 (hardcover) GBP123.00 ISBN: 978-981-3140-96-7 (softcover) GBP65.00 ISBN: 978-981-3140-98-1 (ebook) GBP51.00 This ebook can only be accessed online and cannot be downloaded. See further usage restrictions. Also available at Amazon and Kobo For institutional ebook prices, contact [email protected] ISBN: 978-981-3140-97-4 Also available: Vol. I: Introductory Calculus, Analysis of Functions of One Real Variable Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable Description Chapters Reviews Supplementary 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.