Problems in Real Analysis Advanced Calculus on the Real Axis /

• Κύριοι συγγραφείς: Radulescu, Teodora-Liliana (Συγγραφέας), Radulescu, Vicentiu D. (Συγγραφέας), Andreescu, Titu (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2009.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Differential equations.; Functions of real variables.; Applied mathematics.; Engineering mathematics.; Numerical analysis.; Analysis.; Real Functions.; Numerical Analysis.; Ordinary Differential Equations.; Applications of Mathematics.

 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.