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
This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses. To give a better understanding of the...
This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods...
ANALYSICS MATHEMATICS
Measure and Integral An Introduction to Real Analysis 2nd Edition by Richard L. Wheeden PDF
October 10, 2023
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first...
Recent Posts
- Applied Physics Crash Course by Arthur Beiser PDF
- Variational Principles in Physics by Jean-Louis Basdevant PDF
- Analytical Chemistry by Dhruba Charan Dash PDF
- Handbook of Modern Sensors Physics, Designs, and Applications 3rd Edition by Jacob Fraden PDF
- A Level Physics a for OCR Student Book by Jo Locke PDF
Add Comment