Problems in real analysis: advanced calculus on the real axis

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aimto 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. 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 INDICE: Part I: Sequences, Series, and Limits of Functions.- Sequences.- Series.- Limits of Functions.- Part II: Qualitative Properties of Continuous and Differentiable Functions.- Continuity.- Differentiability.- Part III: Applications to Convex Functions and Optimizatin.- Convex Functions.- Inequalities and Extremum Problems.- Part IV: Antiderivatives, Riemann Integrability, and Applications.- Antiderivatives.- Riemann Integrability.- Applications of the Integral Calculus.- Appendix A: Basic Elements of Set Theory.- Appendix B: Topology of the Real Line.- Glossary.- References.- Index.

• ISBN: 978-0-387-77378-0
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 420
• Fecha Publicación: 01/06/2009
• Nº Volúmenes: 1
• Idioma: Inglés