Problems in Real Analysis: Advanced Calculus on the Real Axis

Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu (auth.)0387773789, 9780387773780

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.

Table of contents :
Front Matter….Pages 1-15
Front Matter….Pages 1-2
Sequences….Pages 3-57
Series….Pages 59-114
Limits of Functions….Pages 115-135
Front Matter….Pages 237-238
Continuity….Pages 139-181
Differentiability….Pages 183-259
Front Matter….Pages 261-262
Convex Functions….Pages 263-287
Inequalities and Extremum Problems….Pages 289-310
Front Matter….Pages 311-312
Antiderivatives….Pages 313-324
Riemann Integrability….Pages 325-372
Applications of the Integral Calculus….Pages 373-414
Front Matter….Pages 415-416
Basic Elements of Set Theory….Pages 417-420
Back Matter….Pages 1-31