Riemann Definition and 619 Threads

Hello, for my FORTRAN class it wants me to use the method of Riemann's sums to find the area under the curve for the function f(x) = -(x-3)**2 +9, and stop when successive iterations yield a change of less than 0.0000001. I know I am going to have to used double precision. I am just confused...

Hi: ____________________________________________________________________ Added Nov.3, 2009 (For anyone who can't read the formula below (probably everyone) and who might have an interest in the subject: - the derivation of two simple equations that locate all the zeros of the zeta...

Riemann sum help! Homework Statement Use Riemann sum with ci= i3/n3 f(x)= \sqrt[3]{x} +12 from x=0 to x=18 n= 6 subintervals Approximate the sum using Riemann's Sum Homework Equations \Sigma f(ci) \Delta xi is the equation for riemanns sum i think The Attempt at a Solution i...

http://img156.imageshack.us/i/17818455.jpg/ http://img215.imageshack.us/i/53355598.jpg/ http://img509.imageshack.us/i/11493310.jpg/ If you look at the above, I have underlined the problem that I am having. So, my first question is, where are these inequalities coming from? If you do have...

Homework Statement Homework Equations The Attempt at a Solution I have attachments that can answer the above template, and please look at the attachments if you are trying to help me. I have two questions regarding upper and lower sums & Riemann sums. So, the attachments 1 & 2 are...

show that in two dimensions, the Riemann tensor takes the form R_{abcd}=R g_{a[c}g_{d]b}. i've expanded the RHS to get R g_{a[c}g_{d]b}=\frac{R}{2!} [g_{ac} g_{db} - g_{ad} g_{cb}]=\frac{1}{2} R_e{}^e [g_{ac} g_{db} - g_{ad} g_{cb}] but i can't seem to simplify it down. this is problem...

i need to show that R_{abc}{}^{e} g_{ed} + R_{abd}{}^{e} g_{ce}=(\nabla_a \nabla_b - \nabla_b \nabla_a) g_{cd} = 0 ok well i know that R_{abc}{}^{d} \omega_d=(\nabla_a \nabla_b - \nabla_b \nabla_a) \omega_c so i reckon that R_{abc}{}^{e} g_{ed} = (\nabla_a \nabla_b - \nabla_b \nabla_a)...

You always see in books that one advantage of the Lebesgue integral over the Riemann integral is that a sequence of continuous functions f_n does not have to converge unifomly to a function f to have: integral of the limit of the sequence = the limit of the integrals of functions in the...

Let me start off by saying I have not yet had a formal course in Number Thoery and have only read briefly on the subject...hence the question: How close (in terms that would be understood by someone in my position) is the math community to proving the Riemann Hypothesis? I'm assuming there...

(i) show that R_{abcd}+R_{cdab} (ii) In n dimensions the Riemann tensor has n^4 components. However, on account of the symmetries R_{abc}^d=-R_{bac}^d R_{[abc]}^d=0 R_{abcd}+-R_{abdc} not all of these components are independent. Show that the number of independent components is...

Can anyone prove the following formula: R_{abf}^{\phantom{abf}e} \Gamma_{cd}^f = R_{abc}^{\phantom{abc}f} \Gamma_{fd}^e + R_{abd}^{\phantom{abd}f} \Gamma_{cf}^e I found it in "General Relativity" by Wald (in slightly different notation).

Hi, I'm Yr 13 and just wanted to do some further reading/exploring. So i understand that the zeta function is something to do with summing up like this: 1/ (1^s) + 1/(2^s) etc etc Now, I just want to know what are non-trivial zeros and trivial zeros? I just want to be able to understand this...

Dear Friends and Colleagues! I have this practise question:- Show that z(sin(z))(cos(z)) statisfies the Cauchy-Riemann Conditions for analyticity for all values of z. Does 1/[z(sin(z))(cos(z))] statisify simiar conditions? Calculate the derivative of 1/[z(sin(z))(cos(z))] at z=0, +...

I recall reading somewhere that Legendre's conjecture implies the Riemann Hypothesis. But the Wiki article suggests that Legendre imposes lighter bounds on the density of primes than does RH, so I would think the other way around, if anything. Thanks for any enlightenment.

Homework Statement Given the following sum, turn it into an integral: \lim_{n \to \infty}\Sigma^n_{k=1}\dfrac{1}{n\sqrt{1+(k/n)^2}} Homework Equations The answer says =\int^2_1\dfrac{1}{\sqrt{1+x^2}} The Attempt at a Solution I understand how to get the equation, but why...

Accurate Proof verification of Riemann’s Hypothesis Riemann Hypothesis states that \int \frac{1}{ln (x)} has a root at \frac{1}{2} when s=2 The time series expansion of Log function is, [tex] \ln(x) = \frac {[x-1}{[x-2}+ \frac{1){3} \frac{x-3}{x-4} + \frac{1}{5}\frac{x-5}{x-6}+……...

Well we know what matryoshka dolls are? Those nested dolls one inside another. I am a mere laymen and amateur that's why I am using descriptive terms instead of math rigor. So what should the approach be: If RH nest Hilbert-Polya conjecture, then what things nest HP conjecture? And ad...

Homework Statement Suppose α(x) increases on [a,b] a≤ x_0 ≤b, α is continuous at x_0, f(x_0) =1 , at all other x in [a,b] f(x)=0. denote ('x knot' as x_0) Prove that f is Riemann Integrable and that ∫fdα=0. Homework Equations Can anyone check my proof or suggest a good method...

To what degree would proving the Riemann hypothesis facilitate the factoring of large composites? In other words, how much would a complete (as opposed to "hit-or-miss") knowledge of primes help to reduce the operations needed to factor large composites?

Hi All, I would like to present what I believe to be a simple way to convey the essence of the Riemann Hypothesis to High School students. I hope you like it, and reply with suggestions for further improvements. Note for teachers: the rationale behind the graphs lays with the geometric...

Homework Statement (x, f(x)) (2,1) (3,4) (5,-2) (8,3) (13,6) A) Estimate f '(4). Show work. B) Evaluate the Intergral from 2 to 13 of (3 - 5f '(x))dx. show work C) Use left riemann sum with subintervals indicated bye the data in the table to apporoximate the intergral from 2 to 13 of...

Looking for a connection to astronomy for a history of mathematics report on 19th century mathematicians. I don't do astronomy. Would like to know of any mathematical developments of Riemann that are used in astronomy that I can understand (which expressly excludes any thing with the word tensor...

Hi There Everyone I am studying undergraduate calculus in first year. My question regards the rules for identifying a limit sum as a Riemann sum and therefore a definite integral. The book we are using says that when choosing \inline \large c_{i} for some f(x) , if \inline \large x_{i -...

http://www.mth.uct.ac.za/omei/gr/chap6/frame6.html" is a derivation of the components of the riemann curvature tensor. the problem is that i can't understand the transition between eq97 and eq89 . what does "To lowest order " mean ?

Homework Statement Suppose f is integrable for all x in[a,b] and f(x)>C ( C is some constant), Must show that 1/f is also integrable. Homework Equations f is integrable implies Upf-Lpf<\epsilon for some partition in [a,b] The Attempt at a Solution Therefore, I must come up...

Hi everyone, For integrable f,g:\left[a,b\right]\rightarrow\mathbb{R} with f(x)\leq g(x) for all x\in\left[a,b\right], it's a basic property of the riemann integral that \[\int_a^b f(x)\,dx \leq \int_a^b g(x)\,dx\] My question is whether the strict version of this inequality holds...

Homework Statement Assume S contained in R2 is bounded. Prove that if S is Riemann measurable, then so are its interior and closure 2. The attempt at a solution Proof: If S is Riemann measurable, its boundary is a zero set. Since the boundary of each open U in the int(S) is part of...

Homework Statement I've been looking at how integrable functions behave under composition, and I know that if f and g are integrable, f(g(x)) is not necessarily integrable, but it -is- necessarily integrable if f is continuous, regardless of whether g is. So I was wondering, what about if g is...

The problem says: evaluate 4x^2+y by breaking into four congruent subrectangles and evaluating at the midpoints, 1=<x<=5 0=<y<=2 When i setup the rectangles these are my coordinates: (1,1/2),(1,3/2),(3,1/2),(3,3/2) and delta A = 2 My answer comes out to be 168...

Homework Statement Suppose f(x):[a,b]\rightarrow\Re is bounded, non-negative and f(x)=0. Prove that \int^{b}_{a}f=0. Homework Equations The Attempt at a Solution I am trying to use the idea that lower sums are zero, and show that the upper sums go to zero as the norm of the...

I read in Elie CARTAN book : "la Géométrie des espace de Riemann" that when R = cte, you can compare space-time to hydrostatic description of a liquid. Is it true ?

One of the axioms of Riemann's geometry holds that there are no parallel lines and that any two lines meet. Since Riemann's geometry fits for that of a sphere, any two great circles of the sphere should intersect. However, if we were to take 2 longitudinal lines, then it is possible that these...

Homework Statement My book presents the Riemann-Darboux integral. It has a small supplemental section on the Riemann integral. Then a later section on the Riemann-Stieljes integral. Then a later chapter on the Lebesgue integral. A supplementary text that I have has a section on...

Homework Statement Write a Riemann sum and then a definite integral representing the area of the region, using the strip shown in the figure below where the upper line is defined by 6x + y = 12 and the other line is defined by y=x^2-4. The figure, which I can't get on here, is just the...

Homework Statement http://img4.imageshack.us/img4/898/integerqj5.jpg Homework Equations The Attempt at a Solution It does appear to be a Riemann sum, I figured the 1/n is probably the width of the intervals and the sum in brackets is related to the sums of the heights of the rectangles. But my...

The characteristic function of the RATIONALS is a well-known example of a bounded function that is not Riemann integrable. But is the characteristic function of the IRRATIONALS (that is, the function that is 1 at every irrational number and 0 at every rational number) Riemann integrable on an...

...But it may not exist yet. Has any mathematician thought about producing a formula or function which spits out all the prime numbers? i.e 1->2, 2->3, 3->3, 4->5, 5->7, 6->11 etc. Any attempts been made? What the closest that people have thought?

If P is the projection map from a Riemann domain M \rightarrow C^n, and U is a connected subset of M with P(U)=B, where B is a ball in C^n, then is P injective on U, so it's a homeomorphism on U? P is locally a homeomorphism by definition. It would be related to B being simply connected...

Homework Statement I am a first-year physics student learning calculus. my question is about the approximation of the area of a region bounded by y = 0. Homework Equations Use rectangles (four of them) to approximate the area of the region bounded by y = 5/x (already did this one), and y =...

Homework Statement I am given a left riemann sum program module in Mathematica and need to convert it into the right riemann sum. The program takes values for x and f/x and the partition and graphs on a certain interval provided. leftRiemannGraph[f_, a_, b_, n_] := Module[{expr}, expr[1]...

Homework Statement I need to find the following: \lim_{n\rightarrow\infty}\left(\frac{1^2+2^2+3^2+...+n^2}{n^3} \right) Homework Equations The Attempt at a Solution I know I could do the sum of the series to find the result but I would like to use Riemann sums. I think I have to start by...

Can anyone provide me with a website that has copies of the original works of Riemann, Taylor, famous mathematicians. I am looking for papers on proved theorems.

in the Riemann Zeta function, is it possible to have two complex zeros off the critical strip that both have the same imaginary part?

Homework Statement Using method of Euler, calculate \zeta(4), the Riemann Zeta function of 4th order. Homework Equations \zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s} Finding \zeta(2): \zeta(2)=\sum_{n=1}^\infty...

Homework Statement Let f be continuous on [a,b] and suppose that f(x) \geq 0 for all x Є [a,b] Prove that if there exists a point c Є [a,b] such that f(c) > 0 , then \int_{a}^{b} f > 0 Homework Equations The Attempt at a Solution Using my books notation, Suppose P =...

Need some urgent help with Riemann Sums. Homework Statement PART A: In all of this question, let I = \int ^{2}_{-2} f(x)dx where f(x) = -2x + 1 Evaluate I. PART B: Use the defintion of the definite integral to evaluate I. i.e Riemann Sum. Homework Equations The...

My assignment: Solve for pi using a Riemann Sum with n= 40,000,000. The function is the antiderivate of 4/(1+x^2) dx. The bounds are from 0 to 1. Solving this gives you pi. Anyone know how to do this? Preferably with fortran77?

Homework Statement Express the integral as a limit of Riemann sums. Do not evaluate the limit. Homework Equations \int_0^{2\pi} x^{2}sin(x)\,dx The Attempt at a Solution I really don't know where to start...any help getting me started would be highly appreciated!

What is an example where it's Riemann integrable int(f(t),t,a,x) but no derivative exists at certain pts?

What's Example of Lebesgue Integrable function which is not Riemann Integrable?