Calculus
Published on 16. February 2023
Book
Paperback/Softback
406 pages
978-1-009-15969-2 (ISBN)
Description
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.
Reviews / Votes
'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 GazetteMore details
Language
English
Place of publication
Cambridge
United Kingdom
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 237 mm
Width: 180 mm
Thickness: 18 mm
Weight
592 gr
ISBN-13
978-1-009-15969-2 (9781009159692)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
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.