Calculus, Volume 2

The second volume of the textbook 'Calculus' meets thedemanding academic standards of engineering and science students. It offers a comprehensive exploration of calculus, designed not only to teach computational techniques but also to foster a deeper conceptual understanding of the subject. What distinguishes this volume is its clear, student-friendly exposition and its emphasis on foundational thinking. The problems are thoughtfully graded-from routine exercises to challenging conceptual puzzles-many inspired by actual coursework and examinations. The book aims to prioritize intuitive explanations and geometric interpretations, helping students develop a strong visual and logical framework for calculus. To enhance engagement, the book also includes real-world applications and historical insights that contextualize mathematical concepts. The book focuses on multivariable calculus, covering limits, continuity, differentiation, and extrema of scalar fields; differentiation and integration of functions of several variables; vector fields and line integrals; Green's theorem and its applications; surface integrals, the divergence theorem, and Stokes' theorem with applications. Inhaltsverzeichnis Limit and continuity of scalar fields.- Differentiation of scalar fields.- Gradient, tangent plane and linearization.- Maxima and minima for scalar fields.- Multiple Integration.- Vector fields.- Line integrals and Green's theorem.- Surface integrals and divergence theorem.- Stokes' theorem and applications. 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.