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This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Contains examples and a large selection of exercises, as well as Notes and Comments.
List of contents
Numbers and Functions.- Sequences.- Continuity and Limits.- Differentiation.- Applications of Differentiation.- Integration.- Elementary Transcendental Functions.- Applications and Approximations of Riemann Integrals.- Infinite Series and Improper Integrals.
About the author
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"Ghorpade and Limaye (both, Indian Institute of technology, Bombay) have written a very coherent and rigorous advanced calculus text on functions of one variable. ... Theorems are carefully proven and exercises (without solutions are provided. ... Recommended. Upper-division undergraduates." ( R. L. Pour, Choice, February, 2018)
"A Course in Calculus and Real Analysis by S.R. Ghorpade and B.V. Limaye (Springer UTM) is a rigorous, well-presented and original introduction to the core of undergraduate mathematics - first-year calculus. ... This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously." (N.J. Wildberger, Gazette of the Australian Mathematical Society, Vol. 35 (3), 2008)
From the reviews:
"The book is a self-contained and rigorous introduction to calculus of one variable. It covers the programme of the first-year in mathematical analysis. The main goal of the book is a clear and successful presentation of the basic ideas of analysis. The reader can see an attention of the authors to help students in understanding and further developing of the basic notions of the subject. ... are illustrated by a number of interesting examples and remarks. In some sense it is a book for self-education." (Sergi V. Rogosin, Zentralblatt MATH, Vol. 1100 (2), 2007)
