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Problem Set 01
Note:
This problem set is due Sep 13 in the class
The following set of problems are devised to check your knowledge in diFerential and
integral calculus, standard electrodynamics, mechanics and gravity.
1.
Integrate the following function:
Z

b

a
dx
±
(
1 +

x

)
x
+

x

+ sin

x

²
where
a
and
b
are two given positive de±nite integers.
2.
²ind
dy
dx
for the following two functions:
y
=

x

sin
x
+

x

x

x

y
=
x
+
x
x
+
x
x
x
+
x
x
x
x
3.
A drop of ink has fallen on a tissue paper.
The drop size increases uniformally and
radially outward on the paper.
In the beginning the rate of increase of the radius of the
drop is almost a constant. However for large time the rate decreases as
t

2
where
t
is the
time measured from the start i.e
t
= 0. Using appropriate considerations ±nd an expression
for the
area
of the drop at
t
=
t
o
. Clearly specify the approximations used to analyse this
problem.
4.
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This note was uploaded on 02/20/2011 for the course PHYS 357 taught by Professor Keshavdasgupta during the Fall '05 term at McGill.
 Fall '05
 KeshavDasgupta
 mechanics, Gravity

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