Sudhir R. Ghorpande and Balmohan V. Limaye
A Course in Multivariable Calculus and Analysis by Sudhir R. Ghorpade and Balmohan V. Limaye is a comprehensive and rigorous introduction to the theory and applications of multivariable calculus. The book develops the subject systematically, beginning with the topology of Euclidean spaces and moving toward differentiation and integration of vector-valued functions. It is written in a formal mathematical style, emphasizing proofs, logical reasoning, and conceptual clarity rather than computational shortcuts. The authors focus on giving readers a deep understanding of fundamental ideas such as continuity, differentiability, gradients, multiple integrals, and line and surface integrals. A distinctive feature of the text is its careful attention to the theoretical underpinnings of calculus, including the inverse and implicit function theorems and Green’s, Stokes’, and Gauss’ theorems. The exposition is detailed and precise, making it suitable for advanced undergraduate or beginning graduate students in mathematics. Numerous examples and exercises are included to reinforce understanding and develop problem-solving skills. The authors, both experienced teachers and researchers, bring a balanced approach that combines formal analysis with geometric intuition. The book serves as an excellent bridge between elementary calculus and advanced analysis or differential geometry. Overall, it is widely appreciated for its clarity, rigor, and the depth of its treatment of multivariable calculus.