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Calculus is an integral and indispensable part of every mathematics course in all universities across the world. It is generally introduced early into the course because of its importance and applicability in other branches of mathematics and other sciences and economics.
This book will be useful to every undergraduate mathematics students, including but not limited to universities in India. The topics covered in this book are also compatible with the Undergraduate Curriculum Framework (UGCF) 2022 based on the National Education Policy (NEP) 2020.
The objective of this book is to present rigorous mathematical analysis in a lucid manner supported by essential examples and illustrations. Although there are several other books on calculus, this book appears fresh owing to its simplicity in its approach and language while strictly maintaining the necessary rigorous mathematical analysis. In fact, this book is a result of many years of teaching and interactions with undergraduate students, and considering and realizing their needs and problems.
Some of the important features of this book are listed below.
- The book covers almost all important topics of differential calculus and the theory of real functions.
- Each topic in the book is presented elaborately to make is comprehensive.
- The book is written in simple easy to understand language and approach.
- Rigorousness of mathematical analysis is maintained throughout.
- A large number of examples and problems are discussed in each topic to help students understand the concepts and their applications clearly.
- Geometrical illustrations are included wherever necessary to enhance the understanding of the topic.
- A large number of interesting and challenging problems are provided as exercises at the end of each chapter for the students to test their progress.
- Answers or hints to each and every exercise problems are included at the end of the book.
- The book adopts internationally accepted conventions and symbols for uniformity.
The author embarked on the teaching career in 2008. With an experience of more than sixteen years of teaching experience in undergraduate mathematics, the author is a faculty in the mathematics department of Shaheed Bhagat Singh College, University of Delhi, since 2010. Currently, he serves as an associate professor in the same institution.
The author has 23 research articles published in reputed peer-reviewed international journals, most of which are indexed in Science Citation Index and SCOPUS Index. Moreover, the author has presented many research articles in international and national conferences, resulting to publications in conference proceedings subsequently. He holds a Doctor of Philosophy (Ph.D) degree in Mathematics from National Institute of Technology Manipur (NIT Manipur). His area of research is complex polynomials, complex analysis, approximation theory, geometric function theory, and has keen interest in analytical number theory as well.
The author has taught a variety of papers in his teaching career, including Calculus, Theory of Real Functions, Riemann Integrations, Sequence and Series of Functions, Real Analysis, Linear Algebra, Partial Differential Equations, Ordinary Differential Equations, C++Programming. He has also contributed in developing study materials for ILLL and SOL, University of Delhi.
1 MATHEMATICAL PRELIMINARIES
2 LIMITS OF FUNCTIONS
3 CONTINUITY
4 UNIFORM CONTINUITY
5 DIFFERENTIATION
6 SUCCESSIVE DIFFERENTIATION
7 MONOTONICITY AND EXTREMA
8 MEAN VALUE THEOREMS
9 EXPANSIONS OF FUNCTIONS
10 INDETERMINATE FORMS
11 PARTIAL DIFFERENTIATION
12 SOME GEOMETRIC PROPERTIES OF FUNCTIONS
13 SINGULAR POINTS AND CURVE TRACING
14 REFERENCES
15 ANSWERS OF EXERCISES
