03460nam 22005775 450 991055274690332120251113205122.03-030-91863-710.1007/978-3-030-91863-7(MiAaPQ)EBC6915725(Au-PeEL)EBL6915725(CKB)21391761400041(PPN)261518755(OCoLC)1303083986(DE-He213)978-3-030-91863-7(EXLCZ)992139176140004120220308d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrier100+1 Problems in Advanced Calculus A Creative Journey through the Fjords of Mathematical Analysis for Beginners /by Paolo Toni, Pier Domenico Lamberti, Giacomo Drago1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (233 pages)Problem Books in Mathematics,2197-8506Print version: Toni, Paolo 100+1 Problems in Advanced Calculus Cham : Springer International Publishing AG,c2022 9783030918620 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.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 atthe 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.Problem Books in Mathematics,2197-8506Functions of real variablesMathematical analysisReal FunctionsAnalysisFunctions of real variables.Mathematical analysis.Real Functions.Analysis.515.8515Toni Paolo57166Lamberti Pier DomenicoDrago Giacomo1914-MiAaPQMiAaPQMiAaPQBOOK9910552746903321100+1 Problems in Advanced Calculus2804396UNINA