This book ontains a collection of challenging problems in elementary mathematical analysis, 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, assumes only a basic knowledge of the topic but opens the path to competitive research in the field, includes interesting and valuable historical accounts of ideas and methods in analysis, presents a connection between analysis and other mathematical disciplines, such as physics and engineering, and be applied in the classroom or as a self-study. 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: (1)Uses competition-inspired problems as a platform for training typical inventive skills; (2)Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis; (3)Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis; (4) Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties. Book is written for classroom or self-study; undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
Type of material - scientific monograph
Publication and manufacture - Dordrecht ; London : Springer, cop. 2009
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