Author: Михаил Абрамян Publisher: Litres ISBN: 5043850507 Category : Mathematics Languages : en Pages :
Book Description
The textbook contains lecture material for the second part of the course on mathematical analysis and includes the following topics: indefinite integral, definite integral and its geometric applications, improper integral, numerical series, functional sequences and series, power series, Fourier series. A useful feature of the book is the possibility of studying the course material at the same time as viewing video lectures recorded by the author and available on youtube.com. Sections and subsections of the textbook are provided with information about the lecture number, the start time of the corresponding fragment and the duration of this fragment. In the electronic version of the textbook, this information is presented as hyperlinks, allowing reader to immediately view the required fragment of the lecture.The textbook is intended for students specializing in science and engineering.
Author: Lynn Harold Loomis Publisher: World Scientific Publishing Company ISBN: 9814583952 Category : Mathematics Languages : en Pages : 595
Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: I. G. Petrovskii Publisher: Courier Corporation ISBN: 9780486697567 Category : Mathematics Languages : en Pages : 142
Book Description
Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Author: Paul M. Gauthier Publisher: Springer ISBN: 3319115111 Category : Mathematics Languages : en Pages : 110
Book Description
This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.
Author: Михаил Абрамян
Author: Max Deuring
Author: Sigurd Angenent
Author: Lynn Harold Loomis
Author: I. G. Petrovskii
Author: James Pierpont
Author: James Pierpont
Author: Bernard Malgrange
Author: Paul M. Gauthier
Author: Giovanni Sansone