This textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the authors forty years of experience in teaching the subject at universities around the world. In this book, Dr. Zalduendo makes use of the history of mathematics and a friendly, conversational approach to attract the attention of the student, emphasizing what is more conceptually relevant and putting key notions in a historical perspective. Such an approach was conceived to help them to overcome potential difficulties in teaching and learning of this subject caused, in many cases, by an excess of technicalities and computations.
Besides covering the core of the discipline real number, sequences and series, functions, derivatives, integrals, convexity and inequalities the book is enriched by side trips to relevant subjects not usually seen in traditional calculus textbooks, touching on topics like curvature, theisoperimetric inequality, Riemanns rearrangement theorem, Snells law, Buffons needle problem, Gregorys series, random walk and the Gauss curve, and more. An insightful collection of exercises and applications completes this book, making it ideal as a supplementary textbook for a calculus course or the main textbook for an honors course on the subject.