Sudhir R. Ghorpade, Balmohan V. Limaye

A Course in Calculus and Real Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. Giving due importance is given to computational techniques and applications, the authors distinguish between the intrinsic definition of a geometric notion and its analytic characterization. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses. Each chapter contains examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 432
• Erscheinungstermin: 14. Oktober 2006
• Englisch
• ISBN-13: 9780387364254
• Artikelnr.: 38208315

Autorenporträt

Sudhir R. Ghorpade is Institute Chair Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He has received several awards, including the All India Council for Technical Education (AICTE) Career Award for Young Teachers and the Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences. His research interests lie in algebraic geometry, combinatorics, coding theory, and commutative algebra. Balmohan V. Limaye is Professor Emeritus in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He is the author of several research monographs and textbooks, including Linear Functional Analysis for Scientists and Engineers (Springer, 2016). He worked at IIT Bombay for more than 40 years and has twice received the Award for Excellence in Teaching from IIT Bombay. His research interests include Banach algebras, approximation theory, numerical functional analysis, and linear algebra. The authors' companion volume A Course in Multivariable Calculus and Analysis (2010) is also in the UTM series.

Inhaltsangabe

1. Numbers and Functions.- 2. Sequences.- 3. Continuity and Limits.- 4. Differentiation.- 5. Applications of Differentiation.- 6. Integration.- 7. Elementary Transcendental Functions.- 8. Applications and Approximations of Riemann Integrals.- 9. Infinite Series and Improper Integrals.- 10. Sequences and Series of Functions, Integrals Depending on a Parameter.- A. Construction of the Real Numbers.- B. Fundamental Theorem of Algebra.- References.- List of Symbols and Abbreviations.- Index.

Rezensionen

"This book would be a valuable asset to a university library and that many instructors would do well to have a copy of this book in their personal libraries. In addition, I believe that some students would benefit if they possessed a copy of this book to use for reference purposes." (Jonathan Lewin, MAA Reviews, April 15, 2019)