User:Egm6321.f12.team4.hong/Report7

Problem R7.1 – Plotting Hypergeometric Function
sec64-9b

Statement
Use matlab to plot F(5, 10; 1; x) near x = 0 to display the local maximum (or maxima) in this region.

Show that

Solution
(a) Matlab Code 

(b) Matlab Result 

(c) Graph 

Author and References

 * Solved and Typed by -- Seong Hyeon Hong
 * Reviewed by --

Problem R*7.3 – Infinitesimal Length in Spherical Coordinates
sec39-1

Statement
Show that the infinitesimal length

can be written in spherical coordinates as follows.

Also, show that the Laplace operator in general curvilinear coordinates,

can be written in spherical coordinates as follows,

Solution
The Eq.(2)sec38-6 can be expanded as below,

and it is given that the Cartesian coordinates, the general curvilinear coordinates and the spherical coordinates have the following relations,

According to the definition of total derivative we can say that,

Therefore if we apply the above equation to find $$dx_1$$, $$dx_2$$ and $$dx_3$$ we get,

Now we square $$dx_1$$, $$dx_2$$ and $$dx_3$$ and add them together to get $$ds^2$$

The result above shows that,

Now if we apply into the Eq(2)sec39-2,

i=1

'i=2'

'i=3'

Therefore now we have the following equation,

Author and References

 * Solved and Typed by -- Seong Hyeon Hong
 * Reviewed by --