実解析問題集 Problems in Real Analysis : Advanced Calculus on the Real Axis

実解析問題集<br>Problems in Real Analysis : Advanced Calculus on the Real Axis

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実解析問題集
Problems in Real Analysis : Advanced Calculus on the Real Axis

Radulescu, T.

ウェブストア価格 ¥18,188（本体¥16,535）
Springer（2009/07発売）
外貨定価 US$ 84.99
ポイント 165pt

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製本 Paperback:紙装版/ペーパーバック版／ページ数 452 p.
商品コード 9780387773780

基本説明

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.

Full Description

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.

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.