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The Big Book of Real Analysis: From Numbers to Measures

Posted By: AvaxGenius
The Big Book of Real Analysis: From Numbers to Measures

The Big Book of Real Analysis: From Numbers to Measures by Syafiq Johar
English | PDF EPUB (True) | 2024 | 950 Pages | ISBN : 303130831X | 103 MB

This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus.

A Short Book on Long Sums: Infinite Series for Calculus Students

Posted By: AvaxGenius
A Short Book on Long Sums: Infinite Series for Calculus Students

A Short Book on Long Sums: Infinite Series for Calculus Students by Fernando Q. Gouvêa
English | PDF EPUB (True) | 2023 | 153 Pages | ISBN : 3031375564 | 13 MB

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.

Tauberian Theory: A Century of Developments

Posted By: AvaxGenius
Tauberian Theory: A Century of Developments

Tauberian Theory: A Century of Developments by Jacob Korevaar
English | PDF | 2004 | 497 Pages | ISBN : 354021058X | 37.4 MB

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.

Functional Analysis: An Introduction to Banach Space Theory

Posted By: AvaxGenius
Functional Analysis: An Introduction to Banach Space Theory

Functional Analysis: An Introduction to Banach Space Theory by Terry J. Morrison
English | PDF | 2000 | 370 Pages | ISBN : 0471372145 | 17.6 MB

A powerful introduction to one of the most active areas of theoretical and applied mathematics.

A Student's Guide to Infinite Series and Sequences

Posted By: roxul
A Student's Guide to Infinite Series and Sequences

Bernhard W. Bach Jr., "A Student's Guide to Infinite Series and Sequences "
English | ISBN: 1107059828 | 2018 | 198 pages | PDF | 3 MB

Advanced Calculus: A Differential Forms Approach

Posted By: AvaxGenius
Advanced Calculus: A Differential Forms Approach

Advanced Calculus: A Differential Forms Approach by Harold M. Edwards
English | PDF | 1994 | 523 Pages | ISBN : 1461266882 | 38.4 MB

My first book had a perilous childhood. With this new edition, I hope it has reached a secure middle age. The book was born in 1969 as an "innovative text­ book"-a breed everyone claims to want but which usu­ ally goes straight to the orphanage. My original plan had been to write a small supplementary textbook on differen­ tial forms, but overly optimistic publishers talked me out of this modest intention and into the wholly unrealistic ob­ jective (especially unrealistic for an unknown 30-year-old author) of writing a full-scale advanced calculus course that would revolutionize the way advanced calculus was taught and sell lots of books in the process.

Fundamentals of Analysis with Applications

Posted By: AvaxGenius
Fundamentals of Analysis with Applications

Fundamentals of Analysis with Applications by Atul Kumar Razdan
English | EPUB | 2022 | 491 Pages | ISBN : 9811683824 | 41.4 MB

This book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology.

Sharpening Mathematical Analysis Skills

Posted By: AvaxGenius
Sharpening Mathematical Analysis Skills

Sharpening Mathematical Analysis Skills by Alina Sîntămărian
English | PDF,EPUB | 2021 | 543 Pages | ISBN : 3030771385 | 43.3 MB

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research.