How does the difference quotient undo what the Riemann sum does or vice versa. In terms of the two formulas?
I would assume that working a difference quotient backwards would be similar to working a Riemann sum forward, but in reality as the operations go this couldn't be further from the...
I have been working on this problem for a while.
I am supposed to prove that
log 2 = \lim_{n \rightarrow \infty} \frac{1}{n+1} + \frac{1}{n+2} + ... + \frac{1}{2^n}.
The problem is that I have a hard time figuring out how I am supposed to prove that something is equal to a transcendental...
so riemann integral pretty much says that if you take closer and closer approximations, then you can find the area of whatever(not too precise, I know, but doing the rectangles and stuff).
I'm looking for a proof of it, but all I can find are more general things, i.e, Riemann integeral is...
Can anyone please direct me in the right way on working out the approximate area of a semi-circle with equation y = (r^2 - x^2)^0.5, by using a Riemann Sum
Could someone explain me what robustness is(in ur words), and how it works in proofs. All i kno is that basically u have two functions and u jiggle them a lot until u make them integrable if its not or destroy their integrability if they are integrable. Geometric explanation would really help...
Hey,
when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field V , ie like this :-
[\bigtriangledown_a, \bigtriangledown_b] = \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a = V;_a_b - V;_b_a
But...
In June of this year the mathematician Louis de Branges published in Internet a proposed "proof" of the Riemann Hypothesis. The page is:
http://www.math.purdue.edu/~branges/riemannzeta.pdf
Years ago De Branges proved the Bieberbach Conjecture. He has tried several times to proof the RH...
So I'm supposed to describe the riemann surface of the following map:
w=z-\sqrt{z^2-1}
I can sort of understand the basic idea and derivation behind the riemann surfaces of w=e^z and w=\sqrt{z},
but ask me a question about another mapping, and I really don't know where to begin. How does one...
Ok, I am told in a complex analysis book that the gradient squared of u is equal to the gradient squared of v which is equal to 0.
We know the derivate of w exists, and w(z)=u(x,y) + iv(x,y)
Thus the Cauchy Riemann conditions must hold. (When I use d assume that it refers to a partial...
Please tell me if I am doing the summation of rectangular areas wrongly.
Using summation of rectangles, find the area enclosed between the curve y = 3x^2 and the x-axis from x = 1 to x = 4.
Now, before I answer the way it asks, I want to use antidifferentiation first to see what I should...
I'm looking for a proof of the Riemann mapping theorem. If I'm not mistaking, there are differnet proofs and the original proof is quite difficult.
I'd appreciate any information on where I can/might find a less complicated proof of this theorem.
let be the product R(s)R(s+a) with a a complex or real number..the i would like to know the limit Lim(s tends to e) being e a number so R(e)=0 ¿is there a number a so the limit is non-zero nor infinite?..thanks.
Does someone here knows something about how tensor of curvature (Riemann) and the hamilton operator associated with a particle are connected ? Makes this question sense ? Thanks
In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions:
Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold? How is this group defined in matrix algebra? Is it a subgroup of GL(4). How do...
Hi there, I have a problem and I was wondering if anyone can help me this one.
Q)Suppose f:[a,b]->R is (Riemann) integrable and satisfies m<=f(x)<=M for all element x is a member of set [a,b]. Prove from the defintion of the Riemann integral that
m(b-a)<=int[f(x).dx]<=M(b-a).
where the...
Hello there, can anyone help me here as I'm finding it difficult to tackle this question.
Consider f(x)=x^3 on the interval [1,5].
Find the Riemann sum for the equipartition P=(1,2,3,4,5) into 4 intervals with x_i^* being the right-hand endpoints (ie. x_i=a+hi)
Then find a formula for the...