About this ebook
The goal of the author is to provide a smoother transition to the understanding of the ideas of infinitesimal quantity, derivative, differential, antiderivative, and the definite integral. In order to give the reader an easier approach to learning and understanding these ideas, the same justifications given by the creators of the calculus are explained in this book.
The justification of the formulas to compute derivatives is deduced according to its historical genesis with the use of the idea of infinitesimal as stated by Leibniz. Also, the justification of the formulas for antiderivatives is explained in detail.
Some applications of the calculus are also covered, among them, extreme values of functions, related rates, arc length, area of regions in the plane, volume, surface area, mass, the center of mass, the moment of inertia, hydrostatic pressure, work, and several more.
Mathematical rigor is not emphasized in this work, but instead, the meaning of the concepts and the understanding of the mathematical procedures in order to prepare the reader to apply the calculus in different contexts, among them: geometry, physics, and engineering problems.
To motivate more teachers and students to use this book, the topics covered have been arranged according to most of the traditional calculus courses. However, because the theory of limits and the definitions of the ideas of calculus based on limits, were created many years later by Cauchy and Weierstrass, the limits and some related ideas (like continuity and differentiability) are not detailed covered.
About the author
Prof. Efraín Soto Apolinar holds a degree in Energy Systems Engineering from the Autonomous University of the State of Quintana Roo, a Master of Science in Systems Engineering from the Autonomous University of Nuevo León, and a PhD in Educational Innovation from the Tecnológico de Monterrey.
He is the author of several books on mathematics and has published articles in scientific journals specializing in Educational Mathematics. In addition, he is the founder of the website Aprende Matemáticas, which offers online mathematics courses, mainly for secondary, high school, and university levels, as well as training programs for teachers in this area.
Since 2002, Dr. Soto has taught mathematics at the secondary, high school, and university level. At the latter level, he has taught engineering students in regular and Honors courses, both in Spanish and English.
He is currently a faculty member in the Department of Sciences at the Tecnológico de Monterrey, Monterrey campus.
