Название: Multivariate Calculus
Автор: Samiran Karmakar, Sibdas Karmakar
Издательство: CRC Press, Levant Books
Год: 2023
Страниц: 330
Язык: английский
Формат: pdf (true)
Размер: 10.8 MB

This book entitled “Multivariate Calculus” is a compilation of all basic topics of Calculus and provides us with the tools to do so by extending the concepts that we find in Calculus, such as the computation of the rate of change to multiple variables, determination of the gradient of a multivariate function by finding its derivatives in different directions, extensive use in Neural Networks to update the model parameters etc. This book is primarily meant for undergraduate and post graduate students.

The treatments of theories are a special feature of this book, which are presented in a systematic and interesting manner. Care has been taken to explain the subject matter in a clear and perspicuous style, so that even an average student can understand it independently. The purpose in writing this book has been to provide a development of the subject matter which is well-motivated, rigorous and up-to-date as best as possible.

This book contains nine chapters including the chapter of Preliminaries (Chapter 0), in which we have tried to make a thorough systematic discussion on this subject. The topics of this chapter have frequently been used in the subsequent chapters of this book.

Sincere attempts have been made to present the topics in a simple and lucid manner to create interest into the subject along with various types of worked out examples. A large number of problems have been suitably framed, properly graded and supplied with answers. Exercises contain motivated problems and are given in right places. Majority of them are straight forward; hints are occasionally given for harder once.

Authors hope that the book will prove useful not only to the Mathematics Honours students for whom it is intended but also to the Engineering students and professionals and to the candidates of different competitive examinations as well.

Topics covered are:

Limits, continuities and differentiabilities of functions of several variables.
Properties of Implicit functions and Jacobians.
Extreme values of multivariate functions.
Various types of integrals in planes and surfaces and their related theorems including Dirichlet and Liouville’s extension to Dirichlet.