Yes, logically it should have only one residue which is zero. However, what I did not understand is why has MATLAB find also a residue which is 1 at the pol z=i/9 ?
I have written this simple code fragment to the MATLAB for finding the residue(s) of the function 1/(z-i/9)^3;
b=[1];
a=[1 -i/3 -1/27 i/(729) ];
[r p k]=residue(b,a)
and get the following result;
r =
0
0
1
p =
0.0000 + 0.1111i
0.0000 + 0.1111i...
yes, your answer is right but I have a question in my mind. Why this is the case? Why at resonance the imaginary part should be zero? I am taking the complex analysis course but have not seen any theorem yet which suggest that the minimum of a complex function occurs where the imaginary part is...
Homework Statement
where C is the contour given with direction marked by increasing y, and where -2≤y≤2 , compute itgeral(z^2-2z+1)dz. With the condition x=5;
Firstly I solved the auestion with the classical way ;
taking z= 5 + it where -2≤t≤2;
we take the i*integral((5+it)^2-2(5+it)...
We are trying to find the roots of a function where exp(f(z)) = c. (where c is a complex number). Also f(z) is a polynomial function. The function will have the following format:
expsolve( [an an-1 …] , c ) where n is the degree of “z”.
For do this I took the natural logarithm of both sides...
I checked it 1000 times. This is the copy of the command window;
>> syms z h;
>> limit((sinh(z+h)-sinh(z))/h,h,0)
ans =
limit((sinh(z+h)-sinh(z))/h,h = 0)
actually this is the problem. The teacher asks us to find the derivative with;
syms x; diff(sinh(x)) and after that finding it with;
syms z h; limit((sinh(z+h)-sinh(z))/h,h,0)
and he wants us to comment on the difference.
With my matlab(R2007a) I find the first result as cosh(z) as...
With the following code segment ;
limit((sin(z+h)-sin(z))/h,h,0)
matlab gives the result cos(z). (which is the differential of the sin(z)).
However, with the code ;
limit((sinh(z+h)-sinh(z))/h,h,0)
matlab gives an absurd result;
limit((sinh(z+h)-sinh(z))/h,h = 0)
newertheless, the...
Homework Statement
Find the set of all points on the surface (y + z)^2 + (z − x)^2 = 16 where the
normal line is parallel to the yz-plane. Describe this set.
The Attempt at a Solution
I find the gradient vector of the surface then I said that the f at f*i should be zero when it is...
I am going to have an calculus exam on saturday. The topic is partial derivatives and double integrals. Does anybody know a website where I could find nice problems about these topics?
Thanks already...
Homework Statement
there is a question and a solution in this page;
http://www.fen.bilkent.edu.tr/~otekman/math102/s03/m2q5.html"
Please firstly examine the question and solution. (5b)...
There it says f(x,y)=z and x=g(r,teta) and y=h(r,teta) and asks fxx.
He solves this problem by...