This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike.

Neatly ties up multivariable calculus with its relics in one variable calculus Caters to theoretical as well as practical aspects of multivariable calculus Contains extensive material on topics not typically covered in multivariable calculus textbooks, such as: monotonicity and bimonotonicity of functions of two variables and their relationship with partial differentiation; higher order directional derivatives and their use in Taylor's Theorem Includes supplementary material: sn.pub/extras

Autorentext

Sudhir R. Ghorpade is Institute Chair Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He has received several awards, including the All India Council for Technical Education (AICTE) Career Award for Young Teachers and the Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences. His research interests lie in algebraic geometry, combinatorics, coding theory, and commutative algebra. Balmohan V. Limaye is Professor Emeritus in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He is the author of several research monographs and textbooks, including Linear Functional Analysis for Scientists and Engineers (Springer, 2016). He worked at IIT Bombay for more than 40 years and has twice received the Award for Excellence in Teaching from IIT Bombay. His research interests include Banach algebras, approximation theory, numerical functional analysis, and linear algebra. The authors' companion volume A Course in Multivariable Calculus and Analysis (2010) is also in the UTM series.

Inhalt
Vectors and Functions.- Sequences, Continuity, and Limits.- Partial and Total Differentiation.- Applications of Partial Differentiation.- Multiple Integration.- Applications and Approximations of Multiple Integrals.- Double Series and Improper Double Integrals.