UID:
almahu_9949272610502882
Umfang:
XVII, 220 p. 171 illus.
,
online resource.
Ausgabe:
1st ed. 2022.
ISBN:
9783030918637
Serie:
Problem Books in Mathematics,
Inhalt:
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 l'Hospital), 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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783030918620
Weitere Ausg.:
Printed edition: ISBN 9783030918644
Weitere Ausg.:
Printed edition: ISBN 9783030918651
Sprache:
Englisch
DOI:
10.1007/978-3-030-91863-7
URL:
https://doi.org/10.1007/978-3-030-91863-7
