A Concrete Approach to Classical Analysis

ISBN-13: 9781441927057 / Angielski / Miękka / 2010 / 433 str.

Springer

Opis

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Recenzje

From the reviews:

"This is an excellent book that gives much more than its modest title suggests. ... What makes this book valuable and unique is the use and development of the more recent ideas in experimental mathematics. ... All in all this is a very exciting list of topics, a book that covers the usual material but from an interesting perspective." (P. S. Bullen, Mathematical Reviews, Issue 2009 g)

"This is an introductory analysis work ... . Combinatorial identities, explicitly discussed, are used to provide analytic results, both estimated and exact; there are interesting presentations on e and ^D*p. The exercises are wide-ranging and frequently challenging ... . for academic curricula, it is a good book to keep on the shelf for its problems and topics. Summing Up: Recommended. Upper-division undergraduates and graduate students." (D. Robbins, Choice, Vol. 46 (10), June, 2009)

Spis treści

Sets and Numbers.- Vector Spaces and Metric Spaces.- Sequences and Series.- Limits and Continuity.- Differential Calculus on R.- Integral Calculus on R.- Differential Calculus on R.- Double Integrals, Triple Integrals, and Line Integrals.- Constants.- Asymptotic and Combinatorial Estimates.