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.

Contains a collection of challenging problems in elementary mathematical analysis

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.