Recent content by reb659

1. Complex analysis antiderivative existence

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...

How so?
3. Differential geometry acceleration as the sum of two vectors

Basically the main question I have is if the only way to do this would be to explicitly calculate the expression for N(t).
4. Differential geometry acceleration as the sum of two vectors

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...
5. Differential geometry acceleration as the sum of two vectors

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...
6. Cauchy riemann equations and constant functions

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...
7. Cauchy riemann equations and constant functions

But what about the function f(z)=z=x+iy? Isn't that function analytic on the say, unit disk with a constant modulus but f is not constant?
8. Cauchy riemann equations and constant functions

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...
9. Linear equations, solution sets and inner products

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...
10. Open and closed intervals and real numbers

Yay! How exactly does uniqueness follow though? It seems like its trivial to prove.
11. Open and closed intervals and real numbers

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...
12. Open and closed intervals and real numbers

Good idea. Isn't it an axiom that if a nonempty subset of R has an upper bound, then it has a least upper bound/sup(S)?
13. Open and closed intervals and real numbers

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...
14. Additive functions, unions, and intersections.

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!
15. Additive functions, unions, and intersections.

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...