Infinite Sequences and Series (Dover Books on Mathematics) by Konrad Knopp (PDF)

Description

One of the finest expositors in the field of modern mathematics, Dr. Konrad Knopp here concentrates on a topic that is of particular interest to 20th-century mathematicians and students. He develops the theory of infinite sequences and series from its beginnings to a point where the reader will be in a position to investigate more advanced stages on his own. The foundations of the theory are therefore presented with special care, while the developmental aspects are limited by the scope and purpose of the book. All definitions are clearly stated; all theorems are proved with enough detail to make them readily comprehensible. The author begins with the construction of the system of real and complex numbers, covering such fundamental concepts as sets of numbers and functions of real and complex variables. In the treatment of sequences and series that follows, he covers arbitrary and null sequences; sequences and sets of numbers; convergence and divergence; Cauchy’s limit theorem; main tests for sequences; and infinite series. Chapter three deals with main tests for infinite series and operating with convergent series. Chapters four and five explain power series and the development of the theory of convergence, while chapter six treats expansion of the elementary functions. The book concludes with a discussion of numerical and closed evaluation of series.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐good basics

⭐Do a series of numbers converge or diverge? That is, does the series you are looking at go on forever, or end in some number? How do sequences and sets relate to each other? Is there a set that contains infinite sequences? From the expansion of elementary functions, to the power series, this book makes your journey into this area of mathematics understandable, even enjoyable. If you are a MathPhile, or want to be, this book is highly recommended.

⭐Learning infinite sequences from this book is not recommended for beginners like me. I suggest reading Calculus by John Stewart where evaluation of limits is demonstrated. Stewart proceeds along with different types of tests compared to this book.This one is more “formula oriented”Regards,Yasir[…]

⭐The original book -which ı have as a pdf- has about 700 pages but the book ı recived has only about 200 pages ı am very disappointed

⭐Nottingham.

⭐Most known series are there

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