Calculus

by Amber Habib

Overview

Calculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski's version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.

Product Details

ISBN-13:	9781009159692
Publisher:	Cambridge University Press
Publication date:	02/16/2023
Pages:	406
Product dimensions:	7.24(w) x 9.37(h) x 0.75(d)

About the Author

Amber Habib is a Professor of Mathematics at Shiv Nadar University (SNU), India. In the past, he was associated with St. Stephen's College in Delhi. His research interests include the representation theory of Lie groups and algebras and mathematical finance. He has contributed to curriculum development at universities such as SNU, Delhi NCR, the Indira Gandhi National Open University, and Ambedkar University, Delhi. He is also the author of The Calculus of Finance and A Bridge to Mathematics.

Table of Contents

Introduction; 1. Real Numbers and Functions; 2. Integration; 3. Limits and Continuity; 4. Differentiation; 5. Techniques of Integration; 6. Mean Value Theorems and Applications; 7. Sequences and Series; 8. Taylor and Fourier Series; A. Solutions to Odd-Numbered Exercises; Bibliography; Index.

Editorial Reviews

‘I thoroughly enjoyed reading this book. For students, it provides a review of familiar topics treated rigorously and an exposure to new and powerful ideas in real analysis. The material is very skilfully woven together with just the right amount of supporting detail and motivation and apposite examples (and counterexamples). And for lecturers, there is much food for thought in the author's innovative approach to what is ostensibly very standard fare, as well as some excellent and well thought-through collections of exercises.’ Nick Lord, The Mathematical Gazette

From the Publisher