A Course in Calculus and Real Analysis

2. Auflage 2018
ISBN: 978-3-030-82741-0
Verlag: Springer Nature Switzerland AG

Buch, Englisch, 538 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 927 g

Reihe: Undergraduate Texts in Mathematics

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. 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Limaye, Balmohan V.

Ghorpade, Sudhir R.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.