“Ghorpade and Limaye (both, Indian Institute of technology, Bombay) have written a very coherent and rigorous advanced calculus text on functions of one. : A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics): Sudhir R. Ghorpade, Balmohan V. Limaye. Request PDF on ResearchGate | On Jan 1, , Sudhir R. Ghorpade and others published A Course in Calculus and Real Analysis.
|Published (Last):||15 November 2011|
|PDF File Size:||12.25 Mb|
|ePub File Size:||9.70 Mb|
|Price:||Free* [*Free Regsitration Required]|
Description This book provides a self-contained and rigorous introduction to calculus of anlysis 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 dalculus circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses calculjs glossed over in real analysis courses.
The Best Books of Check out the top books of the year on our page Best Books of Product details Format Hardback pages Dimensions x x Illustrations note X, p. Looking for beautiful books? Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Other books in this series.
Understanding Analysis Stephen Abbott. Mathematics and Its History John Stillwell. Complex Analysis Joseph Bak. Naive Lie Theory John Stillwell. Introduction to Cryptography Johannes Buchmann. Euclid and Reak Robin Hartshorne. Elementary Analysis Kenneth Allen Ross.
Combinatorics and Graph Theory John M.
A Course in Calculus and Real Analysis : Sudhir R. Ghorpade :
Groups and Symmetry Mark A. Discrete Mathematics Laszlo Lovasz. Elements of Algebra John Stillwell. Back cover copy This book provides a self-contained and rigorous introduction to calculus of functions of one variable.
The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith.
For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles.
Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions.
A Course in Calculus and Real Analysis : Sudhor R. Ghorpade :
A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs.
This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several 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.
Table of contents Numbers and Functions. Review Text “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.
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. It covers the programme of the first-year in mathematical analysis.
A Course in Calculus and Real 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 yhorpade the authors to help students in understanding and further developing of the basic notions of the subject. In some sense it is a book for self-education.
Review quote “Ghorpade and Limaye both, Indian Institute of technology, Bombay have written a very coherent and rigorous advanced calculus text on functions of one variable. Book ratings by Goodreads. Goodreads is the world’s largest site for readers with over 50 million reviews. We’re featuring millions of their reader ratings on courxe book pages to help you find your new favourite book.