Free ↠ Theory and Application of Infinite Series (Dover Books on Mathematics) By Konrad Knopp – Tactical-player.co.uk
This book is one of the dense math books I have read In the first 10 pages it asks Has anyone really beheld the square root of 2 Even if we estimate to the first one million digits, squaring it will not yield 2 It then goes though the fundamentals of number theory and dives in to the complex and rich world of infinite series You will probably have to do some backtracking within the book and on the internet to understand a lot of the finer points in the book It makes you work, but is worth it Unusually Clear And Interesting Classic Covers Real Numbers And Sequences, Foundations Of The Theory Of Infinite Series And Development Of The Theory Series Of Valuable Terms, Euler S Summation Formula, Asymptotic Expansions, Other Topics Exercises Throughout Ideal For Self Study This is a classic book written by Knopp who shows a complete mastery of the subject The construction of real numbers is unique and he uses nests to define them If ever you wanted information on series then this book is a bible on that topic Any student of mathematics must have this in his collection The translator has done an excellent job.Dr Knopp also has a series of books on the theory of complex functions and are highly recommended. This is a very fantastic book on infinite series The coverage of subjects in the book is very comprehensive and goes way beyond a simple introduction to infinite series Reading this book though, I would recommend teaching yourself Real Complex Analysis along with this as it will give you greater insights Overall though I am pleased with this book, and the price cannot be beat. This is a comprehensive book on the 19th century theory of infinite series It is useful mostly for its good examples and its many references to the original writings of mathematicians such as Cauchy, Abel, Dirichlet, Jordan, du Bois Reymond, and Dini There is a chapter on summability methods for divergent series Chapter XIII and a chapter on asymptotic series Chapter XIV.This book is similar to Bromwich s An Introduction to the Theory of Infinite Series. May not be the most modern text on the subject, but it is written clearly and carefully explains the subject The introduction chapter is a very useful refresher for non mathematicians Overall it provides a good treatment of subject, recommended for self study provided you have a reasonable knowledge of calculus and complex numbers for the later chapters.