Problem 2 page 32.
a)
2
ut =a u xx
->the heat equation in one dimension
2
u ( x , t )=
x
2
4a t
e
2 a t
ut :
We calculate first
x2
2
4a t
x 2
2
4a t
2
x
2
4a t
2
2
x
2
4a t
x
2a
d
d
(
)(2a
t)(e
)(e
)
(e )(2a t) (2a t)(e )
2 2
(2 t)
dt
dt
4a t
ut =
=
2
2
3)If the values of x are small then cos x
and this way we have loss of precision in y
We can use this trig identity as remedy
cos =
+ cos
=
+ cos
cos
=
+
+
If x is close to 0 so we have very small values then we can also
2
2
and we get
wh
Introduction
I have chosen to study the demographics in China because this country has the largest
population in the world.Demographics are important in my point of view because they can give you
general information about a population at a given moment in
Introduction:
State your major and why you decided upon this major. If you major is undeclared, discuss possible
majors and why you considered these possibilities. Use resources from the library or online to obtain
two functions (Call these functions Func
xy 6 2
1) ( 4 ) =(x 13 y 61 )2=(x 2 y 5)2=x2(2) y 5(2)=x 4 y10
x y
2) x 210 (x1)(x+ 1)0 x( ,1)(1,1)(1, ) is the domain of the function
x R is the range of the function
3)
-2(x-5)+10=3(x+2)
-2x+10+10=3x+6
14=5x
x=14/5
4) x 2 +5 x7=0(1) x 25 x +7=0 where a=
Function 2 : learning curve of the number of words typed per
minute where t is expressed in weeks
The function:
N (x )=
60 x +180
, x0
x +6
The graph of the function:
Left Riemann Sum for n=4 and interval [0,30]
Midpoint Riemann Sum for n=4 and interval [
Introduction:
State your major and why you decided upon this major. If you major is undeclared, discuss possible
majors and why you considered these possibilities. Use resources from the library or online to obtain
two functions (Call these functions Func
Domain and range
Function 1 : the number of shipments in millions of CD's in
the US from 1998 to 2002 where t corresponds to year 19982002 and 2 t 2 that is :
-for year 1998 we have t=-2
-for year 1999 we have t=-1
-for year 2000 we have t=0
-for year 200
The matrix for the rotation is:
A=
cos -sin
sin cos
The matrix for the reflection is:
B=
cos 2 sin 2
sin 2 - cos 2
So we have a rotation + a reflection after that so that means a combined transformation
and we get :
cos 2 sin 2
cos -sin
cos 2 cos+ sin
7)
a) for : [a,b] - > C where (t) = i*t , 0<=t<=1
f(z) = e^z
(i*t)' = i*t' = i
f(t) = t
f'(t) = 1
b
f
( z ) dz= f ( ( t ) ) ' ( t ) dt
a
1
e
(i t )
i dt =[ e
( i t ) 1
0
]
i
0
i
=e e =e 1=cos ( 1 ) +i sin ( 1 ) 1
0
ix
e =cos ( x )+i sin ( x )
( e (i t ) )
HOMEWORK FOR SAMARA:
10% of 3,644.1=
10% of 1,050=
10% of 34.41=
10% of 744.235=
10% of 10,544.15=
20% of 344.5=
20% of 2045=
20% of 55=
20% of 115=
20% of 3,445=
1 % of 3,665=
1 % of
1 % of
1 % of
1 % of
7,865.56=
4,965.01=
10,665.001=
366.5=
HOMEWORK FO