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＜電子ブック＞
Real Analysis on Intervals / by A. D. R. Choudary, Constantin P. Niculescu

版	1st ed. 2014.
出版者	(New Delhi : Springer India : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XI, 525 p. 36 illus : online resource
著者標目	*Choudary, A. D. R author Niculescu, Constantin P author SpringerLink (Online service)
件　名	LCSH:Integral equations LCSH:Mathematical analysis LCSH:Fourier analysis FREE:Integral Equations FREE:Integral Transforms and Operational Calculus FREE:Fourier Analysis
一般注記	Preface -- Chapter 1. The Real Numbers -- Chapter 2. Limits of Real Sequences -- Chapter 3. The Euclidean Spaces RP and C -- Chapter 4. Numerical Series -- Chapter 5. Metric and Topology -- Chapter 6. Continuous Functions -- Chapter 7. Elementary Functions -- Chapter 8. Differential Calculus on R -- Chapter 9. The Riemann Integral -- Chapter 10. Improper Riemann Integrals -- Chapter 11. The Theory of Lebesgue Integral -- Chapter 12. Fourier Series -- Appendices The book targets undergraduate and postgraduate mathematics students and helps them develop a deep understanding of mathematical analysis. Designed as a first course in real analysis, it helps students learn how abstract mathematical analysis solves mathematical problems that relate to the real world. As well as providing a valuable source of inspiration for contemporary research in mathematics, the book helps students read, understand and construct mathematical proofs, develop their problem-solving abilities and comprehend the importance and frontiers of computer facilities and much more. It offers comprehensive material for both seminars and independent study for readers with a basic knowledge of calculus and linear algebra. The first nine chapters followed by the appendix on the Stieltjes integral are recommended for graduate students studying probability and statistics, while the first eight chapters followed by the appendix on dynamical systems will be of use to studentsof biology and environmental sciences. Chapter 10 and the appendixes are of interest to those pursuing further studies at specialized advanced levels. Exercises at the end of each section, as well as commentaries at the end of each chapter, further aid readers’ understanding. The ultimate goal of the book is to raise awareness of the fine architecture of analysis and its relationship with the other fields of mathematics HTTP:URL=https://doi.org/10.1007/978-81-322-2148-7

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