Table Of ContentA
COMPREHENSIVE TEXT BOOK
OF
APPLIED MATHEMATICS·
I
I
~
Rakesh Gupta
(M.Sc. B.Ed.)
ABHISHEK PUBLICATIONS
CHANDIGARH (INDIA)
(
All rights reserved. No part of this book may be reproduced or transmitted in any form or by
any means, electronic or mechanical, including photocopying, recording or by any information
storage and retrieval system, without permission in writing from the publishers/copyright
owner.
ISBN : 978-81-8247-225-9
Copyright : Author
First Edition : 2009
Publislied by
Abhishek Publications
SCO 57-59, Sector 17-C, Chandiharh.
Phone: 0172-5003768 Telefax: 0172-2707562
e-mail: abhpub@ yahoo.com, www.abhishekpublications.com
Printed at : Shiva Offset. Naveen Shahadra, Delhi
PREFACE _______________________________________ _
This book" A Compresensive Text Book of Applied Mathematics-II" has been
written for the polytechnic diploma level students preparing for a carrier in Engineering.
It covers the latest syllabi of various state boards of technical education in North Region.
The subject has been developed in a systematic, logical and concise form to meet the
requirements of all types of students. The book has been written in a style which makes
it extremely useful for self study. The examples are so arranged that the easier problem
come first and the difficult ones later. At the end of chapter a large number of multiple
choice questions have been provided. This book covers the complete syllabus but some
typical examples in some of the topics have been included to maintain the flow of ideas.
The author lay no claim to the original research in preparing this book. Available sources
on the subject has been used frequently. The subject matter has been arranged in a
proper sequence and presented in a simplified manner.
I feel that no work is perfect and there is always a scope for further improvement
Errors might have been crept in inspite of utmost care. Corrections and suggestions for
further improvement will be thankfully acknowledged and will be implemented in the
subsequent editions.
In last but not least, my thanks are due to my publisher" Abhishek Publications,
Chandigarh", for bringing out this book in such a short period of time. Suggestions for
further improvement of text are again welcome.
Rakesh Gupta
(M.5c. B.Ed.)
Lecturer, S.C.N. Polytechnic,
Chourmastpur, Ambala
SYLLABUS _____________________________________ _
APPLIED MATHEMATICS-II
RATIONALE
Applied Mathematics forms the backbone of engineering discipline. Basic elements
of permutations and combinations trigonometry, vector, complex number and statistics
have been included in the curriculum as foundation course and to provide bases for
continuing education to the students.
DET AILED CONTENTS
1. Co-ordinate Geometry (25 hrs)
1.1 Area of triangle, centroid and incentre of triangle (given the vertices of a
triangle), simple problems on locus.
1.2 Equation of straight lines in various forms (without proof)with their
transformatio~ from to another angle between two lines and perpendicular
distance formula(without proof)
1.3 Circle: General equation and its characteristic's given:
The centre and radius
Three points on it
The Co-ordinates of the end's of the diameter
1.4 Conics (parabola, ellipse and hyperbola), standard equation of conics (without
proof) , given the equation of conics to calculate foci, directrix, eccentricity,
laws rectum, vertices and axis related to different conics Differential Calculus.
2. Differential Calculus (30 hrs)
2.1 Concept of function Four standard limits
Lt x n _ an Lt sin x Lt a x_I Lt
1
------------ - ---- (1 + x)
x
x~a x a 'x->O x 'x->O x 'x~O
2.2 Concepts of differentiation and its physical interpretation
n
Differential by first principle of x , (ax + b)n, Sin x ,Cos x, tan x, cosec x and
x x
cot x, e ,a log x
Differentiation of sum, product and quotient of different functions
Logarithmic differentiation, Successive differentiation excluding nth order
Application of derivatives for (a) rate measure, (b) errors, (c) real root by
Newton's method, (d) equation of tangent and normal, (e) finding the maxima
and minima of a function (simple engineering problems)
3. Integral Calculus (20 hrs)
3.1 Integration as inverse operation of differentiation
3.2 Simple integration by substitution by parts and by partial fractions
3.3 Evaluation of definite integrals(simple problems) by using the general
properties of definite integrals
3.4 Application of integration for Simple problem on evaluation of area under a
curve where limits are prescribed for circle, ellipse, parabola and straight
line calculation of volume of a solid formed by revolution of an area about
axis (simple problems) where limits are prescribed for sphere and cylinder to
calculate average and root mean square of a function area by Trapezoidal
Rule and Simpson's Rule
4. Differential Equations
Solution of first order and first degree differential equation by variable
separation and their simple numerical problem.
CONTENTS ___________________________________ _
Co-ordinate Geometry
1. The Point 3
2. The Straight Line 44
3 The Circle 84
4. The Conic Section 97
Differential Calculus
1. Functions and Limits 137
2. Derivation of Functions 162
3. Tangents and Normals 195
4. Rate of Change of Quantities 209
5. Maxima and Minima 224
Integral Calculus
1. Indefinite Integral 241
2. Definite Integral 321
3. Application of Integration and Numerical Integration 376
Defferential Equations 398
Section I
Co-ordinate Geometry
