Calculus off the Beaten Path

A Journey Through Its Fundamental Ideas

Ignacio Zalduendo (Autor)

Buch | Softcover

XVI, 213 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-15764-6 (ISBN)

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This textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the author's 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, Riemann's rearrangement theorem, Snell's law, Buffon's needle problem, Gregory's 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.

lt;b> Ignacio Zalduendo holds a PhD in Mathematical Sciences (1983) from the University of Buenos Aires, Argentina. He is currently a Full Professor at the Torcuato di Tella University, where he also served as vice-rector (2010-2013). His previous activities include positions as a Visiting Professor at the University of California (UCLA), Complutense University of Madrid, Spain, and Kent State University, in the USA. In 2004, he received a scholarship from the Fulbright Program. Dr. Zalduendo has published over 40 articles and has served as a reviewer for journals as the Journal of Mathematical Analysis and Applications, Annals of Mathematics, Mathematical Reviews, and zbMath. He also authored the book Matemática para Iñaki (in Spanish).

Chapter. 1. The Real Numbers.- Chapter. 2. Sequences and Series.- Chapter. 3. Functions.- Chapter. 4. The Derivative.- Chapter. 5. The Integral.- Chapter. 6. More Derivatives.- Chapter. 7. Convexity and The Isoperimetric Inequality.- Chapter. 8. More Integrals.- Chapter. 9. The Gamma Function.

Erscheinungsdatum	11.11.2022
Reihe/Serie	Springer Undergraduate Mathematics Series
Reihe/Serie	SUMS Readings
Zusatzinfo	XVI, 213 p. 107 illus., 22 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	361 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Archimedes' method • Basel problem • classical inequalities • Derivatives • Gregory's series • integrals • Limits • one-variable calculus • Pappus' theorem • Pythagorean triples • real functions • Riemann's rearrangement theorem • Stirling's formula
ISBN-10	3-031-15764-8 / 3031157648
ISBN-13	978-3-031-15764-6 / 9783031157646
Zustand	Neuware