A Primer on Logarithms by Shailesh Shirali Mathematical Marvels Universities Press

202 Pages·2019·2.07 MB·English

by  Shailesh Shirali

For our entire range of books please use search strings "Orient BlackSwan",
"Universities Press India" and "Permanent Black" in store.
Universities Press (India) Private Limited
Registered Office
3-6-747/1/A & 3-6-754/1, Himayatnagar, Hyderabad 500 029 (A.P.), INDIA
e-mail: [email protected]
Distributed by
Orient Blackswan Private Limited
Registered Office
3-6-752 Himayatnagar, Hyderabad 500 029 (A.P.), INDIA
e-mail: [email protected]
Other Offices
Bangalore, Bhopal, Bhubaneshwar, Chennai,
Ernakulam, Guwahati, Hyderabad, Jaipur, Kolkata,
Lucknow, Mumbai, New Delhi, Noida, Patna
© Universities Press (India) Private Limited 2002
First published 2002
Reprinted 2010
eISBN 978-81-7371-969-1
e-edition:First Published 2015
ePUB Conversion: Techastra Solutions Pvt. Ltd.
All rights reserved. No part of this publication may be reproduced,
distributed, or transmitted in any form or by any means, including
photocopying, recording, or other electronic or mechanical methods, without
the prior written permission of the publisher, except in the case of brief
quotations embodied in critical reviews and certain other noncommercial uses
permitted by copyright law. For permission requests write to the publisher.
Contents
Title Page
Copyright
Preface
Acknowledgements
1 Multiplication
1.1 Early methods
1.2 Napier’s bones
1.3 Multiplication tables
1.4 Interlude on prime factorization
1.5 Parabolic multiplication
1.6 Interlude on nomograms
2 Indices
2.1 The laws of indices
2.2 Big numbers
2.3 The four twos
2.4 Negative exponents
2.5 Fractional exponents
2.6 Exponential notation in science
3 Geometric Series
3.1 The powers of 2
3.2 The powers of 3
3.3 Recurring decimals
3.4 Achilles and the tortoise
4 Logarithms
4.1 Definition
4.2 Genesis of the logarithm
4.3 Brief historical details
4.4 Estimation of logarithms
4.5 Logarithms to base 2
4.6 Common logarithms
5 Computation of Logarithms
5.1 Logarithms in binary form
5.2 Logarithms via square roots
5.3 Interpolation techniques
5.4 Interlude on interpolation
5.5 Using the exponential function
6 Compound Interest
6.1 Interest
6.2 Doubling your money
7 Sensational Stuff
7.1 Stimulus and sensation
7.2 ‘The Versatile Logarithm’–I
8 Measuring Sound
8.1 How do we hear sounds?
8.2 Qualities of sounds
8.3 The decibel scale
8.4 The musical scale
8.5 ‘The Versatile Logarithm’–II
9 Three Applications
9.1 Starry starry night
9.2 Earthquake!
9.2.1 Seismology
9.2.2 The Richter scale
9.2.3 Storm warning
9.3 Sweet and sour
10 The Number e
10.1 Genesis of e
10.2 A graphical approach
10.3 Explanations
10.4 Natural logarithms
11 The Mystique of e
11.1 Derangements
11.2 The nth root of n
11.3 Various series for e
11.4 Continued fractions for e
11.5 The factorial numbers
11.6 Prime numbers
11.7 π and e
11.7.1 Euler’s formula
11.7.2 The “bell curve”
11.7.3 An infinite series plus an infinite GCF
11.7.4 A gem from Ramanujan
11.8 A final comment
12 Miscellaneous Applications
12.1 Radioactivity
12.2 Population growth
12.3 Cooling down
12.4 Parachuting down
12.5 The hanging necklace
12.6 The logarithmic spiral
12.6.1 A brief note on polar coordinates
12.6.2 On spiral forms in nature
12.7 In conclusion
13 An Areal View
13.1 The function L(t)
13.2 Approximate values
13.3 Properties of L(t)
13.4 For which t is L(t) equal to 1?
13.5 Identification of L(t)
A The Irrationality of e
B An Infinite Series for e
C Solutions
Bibliography