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.
- Lucid and structured presentation of concepts for better understanding
- Sufficient practice exercises at the end of each section for self-study
- Additional exercises called tasks and thematic questions for more hands-on practice
- Signage for ease of identification for various sections
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Product details
- Date Published: April 2023
- format: Paperback
- isbn: 9781009159692
- length: 406 pages
- dimensions: 238 x 184 x 19 mm
- weight: 0.6kg
- availability: In stock
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.
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Author
Amber Habib, Shiv Nadar University, India
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.