Problems in Real Analysis: Advanced Calculus on the Real Axis

ISBN-13: 9780387773780 / Angielski / Miękka / 2009 / 476 str.

Teodora-Liliana T. Radulescu; Vincentiu D. Radulescu; Titu Andreescu

Opis

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Recenzje

and includes interesting examples and applications. ... the collection is a very worth-while contribution and should be included in every high school, college, and university mathematics library collection." (F. J. Papp, Zentralblatt MATH, Vol. 1209, 2011)

Spis treści

Sequences, Series, and Limits.- Sequences.- Series.- Limits of Functions.- Qualitative Properties of Continuous and Differentiable Functions.- Continuity.- Differentiability.- Applications to Convex Functions and Optimization.- Convex Functions.- Inequalities and Extremum Problems.- Antiderivatives, Riemann Integrability, and Applications.- Antiderivatives.- Riemann Integrability.- Applications of the Integral Calculus.- Basic Elements of Set Theory.

O autorze

Teodora-Liliana Radulescu received her PhD in 2005 from Babes-Bolyai University of Cluj-Napoca, Romania, with a thesis on nonlinear analysis, and she is currently a professor of mathematics at the "Fratii Buzesti" National College in Craiova, Romania. She is a member of the American Mathematical Society and the Romanian Mathematical Society. She is also a reviewer for Mathematical Reviews and Zentralblatt fur Mathematik.

Vicentiu Radulescu received both his PhD and the Habilitation at the Université Pierre et Marie Curie (Paris 6), and he is currently a professor of mathematics at the University of Craiova, Romania and a senior researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy in Bucharest, Romania. He has authored 9 books and over 100 articles.

Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.

 

 

Blurb

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Key features:

*Uses competition-inspired problems as a platform for training typical inventive skills;

*Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis;

*Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis;

*Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties.