# variations

1. ### Product Sampling variations and types

Product Sampling variations and types St. Louis Blues vs Minnesota Wild Live Stream Anaheim Ducks vs Winnipeg Jets Live Stream NBA Playoffs 2015 Live Stream Milwaukee Bucks vs Chicago Bulls Live Stream New Orleans Pelicans vs Golden State Warriors Live Stream New York Rangers vs Pittsburgh...
2. ### Calculus of variations changing variables

Hi Im am given the functional S[y]=\int_{a}^{b}\frac{x^{3}y^{\prime2}}{y^{4}} dx I am asked to show that if x=u^\beta and with an appropriate value for \beta that S[y]=\int_{B}^{A}\frac{y^{\prime}(u)^{2}}{y^{4}} du So I get...
3. ### Control Theory and Calculus of Variations

Hello, I have a control theory question, its question 1 from the book ´Further mathematics for economic analysis´- I have attached the question with my solution. I want to know if I have solved it correctly, I used the student solution manual but it ony solves up to a certain point. I want to...
4. ### Good book on calculus of variations

I am looking for a book/document (mainly free ones) about calculus of variations of practical nature, i.e. very little theory with many examples and solved problems based on physical applications. Any advice is appreciated.
5. ### Calculus of variations (with a non-smooth integrand)

Hey guys I am currently somewhat stuck on a calculus of variations question. Normally I'd just use the Euler-Lagrange equation, however I am somewhat confused by the max in the integrand. Hence I was hoping whether someone of you could help me to maximise...
6. ### Calculus of variations - showing extremal is minimum

Hi, J[y] = \int_0^1{e^y(y')^2 dx y(0) = 1, y(1) = 2ln(2). I need to find the extremal and show whether it provides a maximum or minimum. In this case I only have problems with the second part. I have the extremal as y(x) = 2ln(x(2-\sqrt{e})+\sqrt{e}). To find whether its a maximum or minimum...
7. ### Calculus of Variations - Noether's Theorem for fields

I am working on the attached problem from the book "Emmy Noether's Wonderful Theorem". I believe I can answer parts a,b,c and d, but I would like help with part e. Now if my answer's to parts a-d are not correct then that might explain why I can't do part e. So I will put some of my working...
8. ### Non square system, system with fewer equations than variations

-45x+18y+ 21z= -12 9x+9y+7z=6 all I have gotten so far is -45x+18y+21z= -12 63y+56z= 18 i know youre supposed to make z=a but I don't know where to go from here. Please help me out and I need the answers ASAP! :)
9. ### Calculus of Variations Rund Trautman Electromagnetism Problem

I have been having trouble with a bunch of examples to do with the Rund Trauman Identity. I have also posted this query on Physics help forum but I generally don't have much luck on that forum. I have the Rund-Trautman identity in this form/notation: \frac {\partial L}{\partial q^ \mu}\zeta...
10. ### Fermat's Principle - calculus of variations

I am attempting the attached problem from Emmy Noether's Wonderfull theorem by Dwight Neuenschwander. I am happy with parts a. and b. For part c I get: H=x_k' p_k - L = \frac {n x_k' x_k'} {r'} - n r' = \frac {n r'^2} {r'} - n r' = 0 It seems quite reasonable to me that H and hence E could...
11. ### Learing variations of the same equations

I'm workig through this book I have and an entire chapter is dedicated to y=mx+b equations. I've learnt a few ways of how to work out the graph. Also the book is teaching me a few different ways in which the equation can be structured. It's getting a bit monotonous and I'm bored of this stuff...
12. ### Calculus of variations with integral constraints

Hi everyone, the image is attached. Both p(x,y) and q(x,y) are probability density functions, q(x,y) is an already known density function, my job is to minimise C[p,q] with respect to 3 conditions, they are listed in the red numbers, 1, 2, 3. Setting up the lagrange function and simplifying...
13. ### Solving an Euler Equation (Calculus of variations)...

I need to solve the Euler equation to make the following integral stationary: \int ( y'^2+\sqrt{y}) dx so I happily assume F = y'^2+\sqrt{y} and find the partial derivative F wrt y' and F wrt y, put both into the Euler equation: \frac{d}{dx}(2y') -\frac{1}{2\sqrt{y}} = 0 Route 1: simple...
14. ### Calculus of Variations (Eulers Equation)

Hello, was wondering if you could help me with a question im stuck on... The functional I is defined by I[y] = integral from 1 to 0 of (1/2 y''^2) dx + (y(1))^2 + y'(1), where y(0) = y'(0) = 0 and y belongs to C^4[0,1]. Show from first principles that a extremum y0(x) of I...
15. ### problem of calculus of variations

Hello everyone I have the following problem. I need to find a function, say f(x), that maximizes \int_{a}^{b}u(x)f(x)dx, where u(x) is the square of the cumulative distribution function of the standard normal minus one half, i.e. u(x)=(\phi(x)-1/2)^2. The maximisation problem does not have...
16. ### Calculus of Variations - proof of Semicontinuity

Dear mathematicians, I would like to ask you if anybody of you could explain me the proof of the theorem of semicontinuity: Let \Omega be an open set in R^n, let M be a closed set in R^N , and let F(x, u, z) be a function defined in \Omega \times M \times R^\upsilon and such that (i) F is...
17. ### Help With a Formula - Multiple Variations

Hello all, I was wondering if someone could lend me a hand. I need to devise a formula that returns a value from another value. For example. The Chicago Bulls have been made 7.5 point favorites over Cleveland In Vegas. If at -7.5 the Chicago Bulls price is 1.91, the price at...
18. ### Calculus of Variations

What is the Euler-Lagrange equation for: I[u] = \int _{- \infty} ^{ \infty} \frac{1}{2} u' ^{2} + \left( 1 - \cos{u} \right) \,dx ? I got that it was u'' = sin(u) but I cannot solve this nicely and this is a question that I should be able to do.
19. ### Calculus of Variations Question

How do you extremise F\left[\mathcal{L}\left(y,\dfrac{dy}{dt},t\right)\right]=f(t)\int_C\mathcal{L}\left(y,\dfrac{dy}{dt},t\right)\,dt
20. ### Calculus of variations

I have a problem relating to the extremal function for a surface of revolution. The Euler-Lagrange equation is {d \over dx}({\partial F \over \partial y'})- {\partial F \over \partial y}=0. Surface area of revolution = \int {2\pi y \sqrt{1+(y')^2}}dx So F(x,y,y') = {2\pi y \sqrt{1+(y')^2}}dx...