ELEMENTARY MULTIVARIATE CALCULUS by Dr. Debasish Sengupta
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Elementary Multivariate Calculus
Dr. Debasish Sengupta
First Published: 2022
ISBN: 978-93-94107-00-7
Pages: 470
CONTENTS
- Functions of Several Variables
- Vector Calculus
- Vector Fields
- Multiple Integrals
- Line, Surface & Volume Integrals
ABOUT THE BOOK:
"Elementary Multivariate Calculus" is intended to serve as a graduate-level course in the study of calculus of functions of several variables. This elementary treatise covers only a part of Real Analysis and is designed to serve as a textbook for students studying mathematics at the advanced level.
The book comprises five chapters. The first chapter contains an in-depth foundation of vector geometry and parametrizations of plane curves, space curves, and spaces, which play an important role in the subsequent chapters. The concepts of real analysis of the functions of several variables are discussed first and then the functions of two and three variables are studied thoroughly in the second chapter. Elementary concepts of vector calculus and vector fields are considered in detail in the third chapter to work with the applications of space geometry. Finally, in the last two chapters, an advanced study of multiple integrals, line, surface, and volume integrals with their various applications in geometry and mechanics are incorporated in a lucid way. Also, every chapter is equipped with a sufficient number of examples along with necessary sketches to gain a clear idea of the concerned problems, some of which are fully solved and the rest are left in the exercises for practice purposes.
The book is sure to be an excellent companion for all aspiring students to enhance their skill of tackling problems in all types of examinations.
Dr. (Prof.) Debasish Sengupta has a brilliant academic record. He has published many research articles on Stability Theory and Eigen-value Problems of a system of second order differential equations with turning points in a number of reputed national and international journals. He has taught many important topics in mathematics, like Advanced geometry of two and three dimensions, Vector algebra and analysis, Advanced higher algebra, Real and Complex analysis, and Differential equations to the students of under-graduate and post-graduate levels at the University of Calcutta.
