Pier Domenico Lamberti is a Full Professor in Mathematical Analysis at the University of Padua, Italy. Toni took an active role in mathematical competitions in his home country, having co-created, directed, and promoted the “Città di Padova” Mathematical Competition, aimed at students of secondary level. He obtained a Mathematics degree (1972) from the University of Firenze and authored a few books, beginning with recreational mathematics. Fermi in Padua, Italy, with prolific research activities on didactics of mathematics. Paolo Toni is a Teacher of Mathematics and Physics, retired from Liceo Scientifico E. 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. Formalism is kept at a minimum, and solutions can be found at the end of each chapter. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided then, related problems are presented. 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. In this work, all the fundamental concepts seen in a first-year Calculus course are covered. 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. 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.
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