100+1 problems in advanced calculus : a creative journey through the fjords of mathematical analysis for beginners / Paolo Toni, Pier Domenico Lamberti, Giacomo Drago.
Toni, Paolo.; Lamberti, Pier Domenico.; Drago, Giacomo.
2022
QA303.2
Available Online

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Title 100+1 problems in advanced calculus : a creative journey through the fjords of mathematical analysis for beginners / Paolo Toni, Pier Domenico Lamberti, Giacomo Drago.
Author Toni, Paolo.
ISBN 9783030918637 (electronic bk.)
3030918637 (electronic bk.)
DOI https://doi.org/10.1007/978-3-030-91863-7
Publication Details Cham : Springer, 2022.
Language English
Description 1 online resource (233 pages)
Item Number 10.1007/978-3-030-91863-7 doi
Call Number QA303.2
Dewey Decimal Classification 515
Summary This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination. In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and lHospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter. Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 18, 2022).
Added Author Lamberti, Pier Domenico.
Drago, Giacomo.
Series Problem books in mathematics.
Available in Other Form 100+1 Problems in Advanced Calculus.
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Summary of basic theory of inequalities
Sets, sequences, functions
Limits of functions, continuity
Differentiation
Classical theorems of differential calculus
Monotonicity, concavity, minima, maxima, inflection points
Graphs of functions
Integrals.

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