The book consists of eight chapters that extensively cover the entire range of differential and integral calculus of multivariable functions.
More specifically, the first chapter introduces the reader to the fundamental elements of analytical geometry and topology, while the second and third chapters present the basic concepts of differential calculus for scalar and vector multivariable functions, such as partial derivatives, operators of divergence, curl, and gradient, the Laplace operator, the Jacobian and Hessian determinants, as well as basic applications of these concepts, such as Taylor expansions, local extrema, applications in analytical geometry, etc.
The remaining part of the book is dedicated to the integral calculus of multivariable functions and sequentially analyzes, through an equal number of chapters, the double, triple, generalized, curvilinear, and surface integrals, as well as the fundamental quantities and theorems related to them (flux and circulation of a vector field, Gauss and Stokes theorems).
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