The book is divided into two parts.

The first part presents an introduction to vector algebra with functions of two and three variables, it includes: continuity, differentiation, and Riemann integration, explained in a simple language so the reader does not require previous deep knowledge of the subject.

The second part provides an ordered and clear approach to Grassmann algebra, it specially focusses on ordinary, Green, Stokes, and Gauss theorems, and some theoretical and practical challenges they have. This algebra is introduced by the robustness of all its operators in the n-dimensional real spaces.

The concise introductory text includes an extensive index and over 150 selected exercises, with different level of difficulty and conceptual questions. These sections make this book essential for readers in upper undergraduate or beginning graduate mathematics courses, who would like to have a solid foundation in calculus for further work in all analysis-based branches of mathematics.

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About the author:

Carlos Polanco is an Associate Professor in the Department of Mathematics at the Universidad Nacional Autónoma de México (UNAM), where he has been a faculty member since 2006. Polanco completed his Ph.D. and his undergraduate studies at UNAM. His research interests lie in the area of high-performance computing, with a focus on the design of mathematical/computational models relating to structural proteomics, and mathematical epidemiology, using clustering, and microchip solutions.

Keywords: Vector calculus, real valued functions, Line integral, Divergence, rotational, surface integral, double integral, triple integral, geometric algebra, exterior product, differential forms

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