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Differential Calculus, Shanti Narayan

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Differential Calculus written by Shanti Narayan.
This book is meant for students preparing for the B.A. and B.Sc. examinations of universities. Some topics of the Honours standard have also been included. They are given in the form of appendices to the relevant chapters. The treatment of the subject is rigorous but no attempt has been made to state and prove the theorems in generalised forms and under less restrictive conditions as is the case with the Modern Theory of Function. It has also been a constant endeavour of the author to see that the subject is not presented just as a body of formulae. This is to see that the student does not form an unfortunate impression that the study of Calculus consists only in acquiring a skill to manipulate some formulae through 'constant drilling'.
The book opens with a brief 'outline of the development of Real numbers, their expression as infinite decimals and their representation by points 'along a line. This is followed by a discussion of the graphs of the elementary functions x"> log x, ex, sin x, sin-1 *, etc, Some of the difficulties attendant upon the notion of inverse functions have also been illustrated by precise formulation of Inverse trigonometrical functions. It is suggested that the teacher in the class need refer to only a few salient points of this part of the book. The student would, on his part, go through the same in complete details to acquire a sound grasp of the basis of the subject. This part is so presented that a student would have no difficulty in an independent study of the same.
(Shanti Narayan)

Book Detail :-
Title: Differential Calculus
Edition:
Author(s): Shanti Narayan
Publisher: S Chand and Company
Series:
Year:
Pages: 429
Type: PDF
Language: English
ISBN:
Country: India

The author Shanti Narayan , Formaly Dean of Colleges, University of Delhi, Delhi. He is an india mathematician and author of many famous math books

All Famous Books of this Author :-
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Book Contents :-
Differential Calculus written by Shanti Narayan cover the following topics.
1. Real Numbers, Variables, Functions
2.Some Important Classes of Functions and their Graphs
3. Continuity and Limit
4.Differentiation
5. Successive Differentiation
6. General Theorems. Mean Value Theorems
7. Maxima and Minima, Greatest and Least values
8. Evaluation of limits. Indeterminate forms
9. Taylor's Infinite Series
10. FUNCTION OF WO VARIABLES Partial Differentiation
11. Some Important Curves
12. Tangents and Normals
13. Derivative of Arcs
14. Concavity, Convexity, Inflexion
15. Curvature, Evolutes
16. Asymptotes
17. Singular Points, Multiple Points
18. Curve Tracing
19. Envelopes
Miscellaneous Exercises II

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