Real Analysis on Intervals

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 worl...

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Bibliographic Details
Main Authors: Choudary, A. D. R., Niculescu, Constantin P. (Author)
Format: eBook
Language:English
Published: New Delhi Springer India 2014, 2014
Edition:1st ed. 2014
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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100 1 |a Choudary, A. D. R. 
245 0 0 |a Real Analysis on Intervals  |h Elektronische Ressource  |c by A. D. R. Choudary, Constantin P. Niculescu 
250 |a 1st ed. 2014 
260 |a New Delhi  |b Springer India  |c 2014, 2014 
300 |a XI, 525 p. 36 illus  |b online resource 
505 0 |a 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 
653 |a Integral equations 
653 |a Mathematical analysis 
653 |a Fourier Analysis 
653 |a Integral Transforms and Operational Calculus 
653 |a Integral Equations 
653 |a Fourier analysis 
700 1 |a Niculescu, Constantin P.  |e [author] 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
028 5 0 |a 10.1007/978-81-322-2148-7 
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082 0 |a 515.45 
520 |a 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