Branch Definition and 217 Threads

You can choose to limit yourself to continuous or analytical functions

dy/dx = (4x - y)/(x + 2y) for y(0) = 1 As not seperable us y = vx where v is a funciton of x method. If you follow it through you'll get y as a quadratic. According to the answer scheme, I should take the +ve square root because of y(0) = 1... why? Why can I discard the -ve square root...

Hi all, I've reason to believe that the function f(q)=\int\frac{d^{4+n} k}{(2\pi)^4}\frac{1}{(a \cdot k -i \epsilon) (b \cdot k -i \epsilon) (k^2 -i \epsilon) ((q-k)^2-i\epsilon)} where a, b are real -valued 4+n component vectors; epsilon is real, positive and infinitesmal, and taken to zero...

I'm a physics student and I graduate in a few months. I have been looking for PhD's because I want to carry on learning physics but have so far struggled to find a PhD subject that really caught my eye. I do, however, have an interest in the brain, the mind and consciousness (although I have no...

Which field of physics would i categorize this in? I am interested in the study of biofuels, photovoltaic cells, and grid tie inverters. Please give me the field that each corresponds to. Also, what are some other interesting/complex problems in those fields? Or rather I'm mainly interested in...

I'd like to work into integrating sensors/programs to robots and machines to "connect" the parts together and make them work. Ex: I don't want to design the hydraulics or mechanical parts, I'd like to be the guy that connects ****, integrate the controls AND make everything work together...

Hello! I am about to be ready with my bachelor degree in physics. I became lately interested in mathematical physics. I wonder which courses I should take (are most suitable and usefull) in order to continue with mathematical physics in the future? Thanks

What is up people? I was wondering if you could help me find exactly what's the type of math I need to do solve these kinds of problems... Let's say I have 65% chance of my business being a complete success and had $200,000, how do I work out the optimal amount to put into the business...

That's why science degrees are called "PhD," which means doctor of philosophy. Comment?

Just out of curiosity.

I want to become a chemical engineering. But some body says there is no opportunuites for chemical engineers. My opinion is to do chemical engineering only. Please tell me is it good or bad? what are the opportunities ?

Which engineering branch should i choose!? Hi i want to do undergraduate degree from India in engineering and post graduate course from america. Since i was small i was interested in space technology, so what are the branches (apart from aerospace and aero nautical ) in which i can further do...

I've had some arguments after I assumed ( perhaps wrongly) that electric fields were responsible for the direction that branches grow in. In any case my inquires on this all result in the same answers. That the direction of growth is determined by light and gravity. Do all you agree with...

This may be a strange question, but humor it if you would. I have perhaps watched one too many science fiction shows, but I digress. If one wanted to get into a field, say, involving cyborgs or some such, what would that be? What if one wanted to put a brain or transfer consciousness into a...

Homework Statement I'm finding the residues of the branch cut of \int^\infty_0 \frac{dx}{x^{1/4}(x^2+1)}dx Homework Equations The Attempt at a Solution I am trying to find the residue of i I am not sure how to handle lim z->i of \frac{1}{z^\frac{1}{4}(z+i)} Any nudges...

Homework Statement Suggest how the energy difference arises between the optic and acoustic branches in a 1d diatomic chain.Homework Equations The Attempt at a Solution I know that on the optic branch atoms oscillate in anti-phase within the unit cell and in phase in the unit cell on the acoustic...

Homework Statement Branch cut for cos(sqrt(z)). Homework Equations The Attempt at a Solution Apparently there is no need for a branch cut for this function, but I am not sure why - I heard it has something to do with cos being an even function. Any clarification would...

Hi guys, I need to show that: \int_{0}^{\infty } \frac{x^{a}}{(x+1)^2} \dx = \frac{\pi a}{\sin(\pi a)} , where -1<a<1. The problem is, that although a hint is given,the path of integrating it, I have difficulty what they really mean with "cut line, branch points, multivalued functions" etc...

Every few years I Google this book and then ask about it book here on PF on the off-chance that someone recognizes it. I cannot nail down anything specific that Google can work with, so ultimately it fails. I'm going to try something different this time that should improve my Google search...

Homework Statement The function f(z) = (1-z2)1/2 of complex variable z is defined to be real and positive in the range -1 < z < 1. Using cuts running along the real axis for 1 < x < infinity and -infinity < x < -1, show how f(z) is made single valued and evaluate it on the upper and lower...

Homework Statement The function f(z) = (1-z2)1/2 of the complex variable z is defined to be real and positive on the real axis in the range -1 < x < 1. Using cuts running along the real axis for 1 < x < infinity and -infinity < x < -1, show how f(z) is made single-valued and evaluate...

In my lifetime, there will be at least two major challenges to human society: climate change (of which you have hopefully heard) and peak oil (of which not enough people are talking). The first necessitates decreasing emissions, going green, reducing consumption, likely a reorganizing of human...

Homework Statement f(z)=\sqrt{(z.^3+8)} How many branches (solutions) and branch points does the funtion f(z) have? Homework Equations The first part of the question was working out the roots of z^3+8=0 which I found to be -2, 1+i\sqrt{3} and 1-i\sqrt{3} The Attempt at a Solution...

In the expression ln(-s^2-i\epsilon) , s^2 and \epsilon are positive (this expression can result from for example a loop diagram where s^2 is a Mandelstam variable). In mathematics, the branch cut of ln() is usually taken to be the negative real axis, so that the value above the negative axis...

Homework Statement Homework Equations V=ir E=V-ir The Attempt at a Solution First part is solved. The EMF of the battery is higher than the actual output voltage due to the internal resistance of the battery. E=11.25, V measured is 10.5. The second part is boggling my mind...

Homework Statement define a branch of sqrt(1+sqrt(z)) and show that it is analytic Homework Equations The Attempt at a Solution Need some help solving this one...

Suppose you're trying to provide a branch cut in \mathbb{C} that will define a single-value branch of f(z) = \log(z - z_0). I don't know where to begin. Can someone help explain this concept to me?

in the areas of research in grad school, what areas uses statistical mechanics the most? condensed matter? astrophysics?

I'm still undergraduate and want to explore various branches of physics. I just feel that I like theory more and that's it. However I'm curious which branch of theoretical physics allows you to explore fundamental aspects of universe. I've heard that String Theory, QG, HEP etc. only sound sexy...

The phrase 'Coulomb branch' appeared several times in a paper on M-branes, but I don't know its meaning. Is there anyone who explain it for me? Thanks.

1.I am trying to evaluate the \int\frac{ln(x)}{(x^{2}+1)^{2}} from 0 to inf2. I think I am having problems defining what my branch cut should be. 3. Here is what I have tried to no avail. First set the branch cut from -infty to 0. Then changing it to a contour integral gives us...

Hi, I find integration with branch cuts difficult to grasp. For example, I can understand that \sqrt{x} is mutivalued and has 2 branches if we take a branch cut from 0 to +infty. But given it to be integrated from -infty to +infty what is the the meaning of taking a branch of \sqrt{x} ...

Homework Statement Calculate the current in each branch of the circuit bellow? The Circuit: http://picasaweb.google.com.au/hilly1989/ElectronicsDiagrams#5317672833283799074 Calculated currents using Multisim: http://picasaweb.google.com.au/hilly1989/ElectronicsDiagrams#5317672834037978066...

i need help finding the limits above and below the branch cut segment of sqrt(z^2-1) for -1<x<1 I always get total phase above is pi/2 and total phase below is 3pi/2 but this is wrong please help

Hi everyone, I have a couple questions that have been gnawing at my head for some time: Why is it that on wikipedia for the example logarithms and residue at infinity, (on the methods of conour integration link) that the integral is not zero? there are no isolated singularities inside the...

Hey guys, I need to find the branch cut of the function f(z) = Log[z^2 +9] where the negative real axis has been removed from the domain of the log function. Now this is the bit that confuses me, is this saying that we must ensure that no negative real components enter the argument of the log...

Here's a question my mate asked me to help out with, but I'm a bit stuck, any help would be good. Apologies for not being able to show the circuit (don't know how) so I'll explain it. A parallel circuit has a supply of 1 Vrms and has 2 branches. The first branch has a single capacitor of 2.2...

Homework Statement Define the branch cut prior to solving the following: integrate from 0 to infinity of [log x]^4/ [1+x^2] Homework Equations The only poles inside the upper half plane is i The Attempt at a Solution How do I separate the countour?---help. Thanks.

I have a question with regards to branch cuts: Say I have a function f(z) = log(z2 - 1). Why is a simple branch cut connecting z = -1 and z = +1 not sufficient to define an analytic function? On the other hand, why is it sufficient for the function f(z) = (z^2 - 1)^(1/2) ? This is in the...

Refering to the http://lab.artematrix.org/images/PIPE_BRANCH.jpg" , my question is: How to calculate volume B? Please note, volume C is not to be considered part of volume B, it is included just to illustrate one of the boundries of volume B (the yellow liquid is just about to flow over...

So...Im a first year student doing civil engineering atm. I passed everything in the first semester (1 70, the rest were 60s except for 50 on the dot for app maths...we did mess around a lot and skipped many lectures so i shouldve done better i guess), second semester has just started. Gotta say...

(1-z^3)^{1/2} has three branch points at z=1, z=\omegaand z=\omega^2 where \omega = e^{2\pi i/3} The branch points are the zeros of the function correct? So why are not z=\omega^4, z=\omega^6, z=\omega^8 etc also branch points as they are zeros of the function? as (e^{2\pi i/3^3})^6...

Friend,this year in 2008 , i am going to take admission in engineering undergraduate program in india.In India there is no scope for nanotechnology/nanoelectronics. Which branch should i choose during Btech/BS, so that it will be helpful in learning nanoelectronics during MS?For financial...

Mechanical or Electrical? Also, is a course in optimization useful? This does not necessarily pertain to engineers. If so, in what other fields? Besides applied mathematics/numerical analysis.

How does soluble groups fit into algebra? Why is there another name for it called solvable groups? What branch does it fall under?

Homework Statement A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground. (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has...

A friend of mine is a GRist and once explained to me that geometry is a branch of physics because the basic knowledge of geometry comes from observing nature. He's a bright guy who explains things well. I happen to agree with him. I forgot how he so elegantly put it though. I also read it...

I have been going back and forth about going into mechanical or electrical engineering. i want to use a lot of math in my daily activities, so I am thinking possibly electrical. which one ( if any ) has more job openings could someone possibly compare and contrast the two breifly for me...

Homework Statement A bird lands near the tip of a branch and it is observed that initially it oscillates up and down, about once per second. Estimate how far the tip of the branch will be below its equilibrium position once the bird comes to rest. Homework Equations Newton's second law...

hi, just wondering which branch of physics holds the most mathematics. because i love finding and using mathematic formulas. etc. Thankyou, Bye.