Calculus, Volume 1

The first volume of the textbook 'Calculus' is designedspecifically to meet the rigorous academic standards of engineering and science students. The book is a comprehensive exploration of calculus, tailored not just to teach computational techniques, but also to cultivate a deeper conceptual understanding of the subject. What sets the book apart is its clear, student-friendly exposition and its emphasis on foundational thinking. The problems are thoughtfully graded, ranging from routine practice to challenging conceptual puzzles, many of which are modelled after the actual coursework and examination. The book aims to focus on intuitive explanations and geometric interpretations, helping students build a visual and logical framework for calculus. It also includes real-world applications and historical notes, making the subject more engaging. This volume covers all essential topics-limits, continuity, differentiation, integration, sequences, and series, with real-world applications and historical context. Inhaltsverzeichnis Numbers, functions and sequences.- Limit and continuity.- Differentiation.- Maxima, minima and curve sketching.- Approximations.- Integration.- Logarithmic and exponential functions.- Applications of Integration.- Series of numbers and functions. Autorenportrait Inder Kumar Rana is a distinguished mathematician andeducator, renowned for his contributions to mathematical analysis and mathematics education in India. He served as a Professor in the Department of Mathematics at IIT Bombay from 1984 to 2015, and later continued as an Emeritus Fellow. He has authored several influential books, including An Introduction to Measure and Integration, From Numbers to Analysis, Calculus @IITB: Concepts and Examples, and From Geometry to Algebra: A Course in Linear Algebra. He also developed interactive web courses and video lectures on topics such as Calculus, Linear Algebra, and Measure Theory, significantly advancing math pedagogy. Prof. Rana's excellence has been recognized with multiple awards that include C. L. Chandna Mathematics Award (2000) for outstanding contributions to research and teaching; Excellence in Teaching Award (2004) from IIT Bombay and Aryabhata Award (2012) from the All India Ramanujan Math Club for his work in mathematics education.