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"Calculus is an area of advanced mathematics in which continuously changing values are studied. It is introduced at the school level and usually school students consider it as a set of tricks that they need to memorize. They study many other sub-areas of mathematics like algebra and real functions, but are unable to correlate calculus to these streams. This book is a good resource to understand the correlation. It is written to support students in this transition from school calculus to university analysis. Calculus is intended for students pursuing undergraduate studies in mathematics or in disciplines like physics and economics where formal mathematics plays a significant role. It provides a thorough introduction to calculus, with an emphasis on logical development arising out of geometric intuition. For students majoring in mathematics, this book can serve as a bridge to real analysis. For others, it can serve as a base from where they can venture into various applications. After mastering the material in the book, the student would be equipped for higher courses both in the pure (real analysis, complex analysis) and the applied (differential equations, numerical analysis) sides"--
List 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.
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.
Summary
This book is designed for students pursuing undergraduate studies in mathematics or disciplines like physics, economics, and engineering where formal mathematics is important. The author has blended geometric intuition and algorithmic thinking with formal proofs, providing a bridge from school calculus to university analysis.
