University of Florida/Egm6341/s10.team3.aks/HW2

(4) Derive the composite trapazoidal rule and composite simpson's rule from simple trapazoidal and simple simpson's rule edit

Ref Lecture notes p.9-3

Problem Statement edit

Show Simple Trapazoidal rulep.7-1 Composite Trapazoidal rule p.7-1

and

Show Simple Simpson's rule p.7-2 Composite Simpson's rulep.7-2

Solution edit

Composite Trapezoidal rule

From Simple trapezoidal rule we have ,


similarly we have

. . . .

Summation of all of above expression gives

Hence Proved..

Composite Simpson's Rule

From Simple Simpson's rule we obtain ,

where

Similarly

. . . .

After Summation of above terms we obtain


where n = 2k and k = 1,2,3,4.....

Hence Proved

(14) Prove edit

 

Ref Lecture p.15-2

Problem Statement edit

Prove that

 

where

 


Solution edit

 

 

 

 

 

   

 

 

Hence Proved ..

(12) Show Derivation edit

 

Ref: Lecture Notes p.15-1

Problem Statement edit

Show derivation that

 

Solution edit

From (4) in p.14-2, we can write down the expression of  

Given :

f(x(t)) = F(t)

Let there exists  

 

 

 

but  

 


Hence Proved ,