100+1 problems in advanced calculus : a creative journey through the fjords of mathematical analysis for beginners / Paolo Toni, Pier Domenico Lamberti, Giacomo Drago.
2022
QA303.2
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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.)
3030918637 (electronic bk.)
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.
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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.
Drago, Giacomo.
Series
Problem books in mathematics.
Available in Other Form
100+1 Problems in Advanced Calculus.
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Table of Contents
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.
Sets, sequences, functions
Limits of functions, continuity
Differentiation
Classical theorems of differential calculus
Monotonicity, concavity, minima, maxima, inflection points
Graphs of functions
Integrals.