A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn’t and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren’t usually found in books of this type. It includes proofs of the irrationality of e and ?, continued fractions, an introduction to the Riemann zeta function, Cantor’s theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject.
Limits, Limits Everywhere The Tools of Mathematical Analysis Free Download
October 16, 2022

You may also like
Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner’s Trigonometry. This...
Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader’s part and develops the subject fully. Volume I...
The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and...
Recent Posts
- Mathematics with Applications in the Management, Natural, and Social Sciences 11th Edition by Margaret L. Lial PDF
- Intermediate Algebra 2nd Edition by Margaret L Lial PDF
- Mad About Modern Physics Braintwisters, Paradoxes, and Curiosities by Franklin Potter PDF
- Calculus with Applications, 11th Edition by Margaret L. Lial PDF
- Physics for Scientists and Engineers with Modern Physics 4th Edition PDF
Add Comment