Homework Statement
a) Does f(z)=1/z have an antiderivative over C/(0,0)?
b) Does f(z)=(1/z)^n have an antiderivative over C/(0,0), n integer and not equal to 1.
Homework Equations
The Attempt at a Solution
a) No. Integrating over C= the unit circle gives us 2*pi*i. So for at least...
So I should able to write a(1) as a linear combination of T(1) and N(1), correct?
But how do I get N(t)? Taking derivatives of T(t) is very messy and the professor said it didn't involve any long calculations. Furthermore we haven't learned about the binormal and normal in this section yet...
Homework Statement
a(t)=<1+t^2,4/t,8*(2-t)^(1/2)>
Express the acceleration vector
a''(1) as the sum of a vector parallel to a'(1) and a vector orthogonal to a'(1)
Homework Equations
The Attempt at a Solution
I took the first two derivatives and calculated a'(t)=<2t, -4t^2...
Ah yes, I meant unit circle. I was thinking the domain would need to have restrictions because I thought I proved it yet found a counterexample at the same time. But for the original problem:
Let f=U + iV. We have |f|=c for some constant c. |z|^2=zz*, so we have |f|^2=c^2 which implies...
Homework Statement
Let f(z) be analytic on the set H. Let the modulus of f(z) be constant. Does f need be constant also? Explain.
Homework Equations
Cauchy riemann equations
Hint: Prove If f and f* are both analytic on D, then f is constant.
The Attempt at a Solution
I think f need...
Homework Statement
Let W be the subspace of R4 such that W is the solution set to the following system of equations:
x1-4x2+2x3-x4=0
3x1-13x2+7x3-2x4=0
Let U be subspace of R4 such that U is the set of vectors in R4 such the inner product <u,w>=0 for every w in W.
Find a 2 by 4...
So far:
Since S is bounded above and below, by Dedekind completeness there exists a supremum of S. Call it b. Again by dedekind completeness we can say there exists an infimum of S. Call it b. By definition of sup and inf, a<b. We are left to show a,b are unique and that S is exactly one...
Homework Statement
Show that:
Let S be a subset of the real numbers such that S is bounded above and below and
if some x and y are in S with x not equal to y, then all numbers between x and y are in S.
then there exist unique numbers a and b in R with a<b such that S is one of the...
I am such an idiot. I tried it before representing the left hand side as a union of disjoint sets but for some reason I didn't bother manipulating the right hand side in the same way.
Thanks a ton!
Homework Statement
A function G:P--->R where R is the set of real numbers is additive provided
G(X1 U X2)=G(X1)+G(X2) if X1, X2 are disjoint.
Let S be a set, Let P be the power set of S. Suppose G is an additive function mapping P to R. Prove that if X1 and X2 are ARBITRARY(not necessarily...