What is Branch: Definition and 215 Discussions

A branch (UK: or UK: , US: ) or tree branch (sometimes referred to in botany as a ramus) is a woody structural member connected to but not part of the central trunk of a tree (or sometimes a shrub). Large branches are known as boughs and small branches are known as twigs. The term "twig" often refers to a terminus, while "bough" refers only to branches coming directly from the trunk.
Due to a broad range of species of trees, branches and twigs can be found in many different shapes and sizes. While branches can be nearly horizontal, vertical, or diagonal, the majority of trees have upwardly diagonal branches. A number of mathematical properties are associated with tree branchings: they are natural examples of fractal patterns in nature, and, as observed by Leonardo da Vinci, their cross-sectional areas closely follow the da Vinci branching rule.

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  1. P

    Which branch of Engineering Technology?

    Hey, I thought I'd just throw this out to the forum to hear some opinions. I'm considering doing an Engineering Technology Diploma here in Canada and I'm just debating which branch to choose based on my interests and experiences. The branches I'm looking at are Electrical Engineering...
  2. S

    Find all branch currents in the network shown.

    Homework Statement The problem and its solution are attached. Homework Equations V = RI R_eq = 1/R_1 + 1/R_2 + ... + 1/R_n (Parallel circuits) R_eq = R_1 + R_2 + ... + R_n (Series circuits) The Attempt at a Solution For the two lines of math below “Now referring to the reduced...
  3. E

    Branch points and cuts of multivalued function

    Homework Statement This problem is on how to identify the branch points and the branch cuts of a multivalued function. Consider the following function f(z)=Log(1+z^\alpha) where \alpha is a rational number and z\in \mathcal{C}.Homework Equations Obviously, for the function z^\alpha, it has...
  4. E

    Integration with branch cuts and singular points

    Homework Statement Prove that \int_0^{\infty} \frac{x^{1/\alpha}}{x^2-a^2} dx = \frac{\pi}{2a}\frac{a^{1/\alpha}}{\sin(\pi/a)}\left(1-\cos(\pi/\alpha)\right) where a>0 and -1<1/\alpha<1 Homework Equations It is apparent that there are two first order singular points at x=a and x=-a...
  5. Doofy

    Physics How easy/common is it to move from one branch of physics research to another?

    I'm currently a phd student and am doing high energy particle physics. I am unsure about what I will do when I graduate, but I suspect I willl apply for postdoc positions. What I'm wondering is, let's say I do decide to stay in physics. Am I completely limited to a career in HEP physics, or...
  6. N

    Mellin's inversion integral, branch cut problem

    I recently had to solve a problem in which i had to find the inverse laplace transform of some function with a branch cut from - ∞ to 0, so i used a contour avoiding that branch cut like this http://www.solitaryroad.com/c916/ole19.gif my problem is as follows: i know the contributions from...
  7. C

    Which branch of statistics and mathematics deals with extrapolations?

    Which branch of statistics and mathematics deals with extrapolations and trend analysis? That is, where one can estimate various trends (be they exponential, linear, etc.) that apply to our data and draw a trend which could extrapolate the future variation. Am I referring to the time series...
  8. N

    Definition of electrical branch

    Hi everyone! I wanted to know why in the circuit analysis a generator doesn't represent an electrical branch? And the second question is if two resistors are in series on a wire, does it represents only a branch(the series of the resistance) or two branches ?
  9. C

    Branch cuts in complex analysis

    Homework Statement Given that the standard square root sqrt(anything) has a branch cut from (-inf,0), find the branch cuts of the following: z+sqrt(z^2-1) z+isqrt(1-z^2) z+sqrt(z+1)sqrt(z-1)Homework Equations The Attempt at a Solution I understand what branch cuts do (multivalue functions ->...
  10. W

    Is probability branch of maths or stats?

    Hi all, I was wondering if someone can tell me that is probability branch of mathematics or statistics. Wikipedia says that Probability Theory is branch of mathematics but in University Statistics department offers probability modules. Also, is Statistics branch of mathematics, after all it...
  11. M

    Why are non-intersecting branch cuts necessary for multiple-valued functions?

    Why is it necessary that branch cuts for multiple-valued functions are non-intersecting? Does this have to do with needing each sheet for one value (ex. for positive/negative square roots)?
  12. Spinnor

    Odd looking pine tree, one branch did not follow the rules?

    Walking the dog takes me past an odd (to me) looking pine tree. I live in south eastern Pennsylvania. With help of Google I think the tree in question is a White Pine, see http://www.oplin.org/tree/fact%20pages/pine_white/pine_white.html Also see the images below of the tree. I don't think...
  13. V

    What branch of math deals with nonlinear systems?

    Like linear algebra goes in depth about linear systems, what should I look for to learn about the extension of linear algebra to nonlinear systems? Is there a name of the field of study? If I go into a book store to buy books about it, what should I be looking for? Abstract Algebra? Complex...
  14. I

    Improper Integral With Branch Cut

    I understand most of the problem, but have yet to understand where a particular term came from. The problem is as follows: Homework Statement Show that (0 to ∞)∫dx/[(x2+1)√x] = π/√2 Hint: f(z)=z−1/2/(z2+ 1) = e(−1/2) log z /(z2+ 1). The Attempt at a Solution I actually have a solutions...
  15. V

    Which engineering branch is good for research works in future?

    I am from India.. I want a branch which has significant room for research works in future after B tech Mtec and so on.. Right now my preference is Electrical and electronics,Electronics &Ccommunication,Electrical Engineering, Computer Science.(need further suggestions from u)... Is it good or...
  16. J

    What Branch Should I Choose for My Science Studies?

    I am in a dilemma over which branch should i take? I find all the subjects interesting : physics, maths , physics , biology Initially i decided to take physics and become a physicist but after reading the forums here i should better take engineering. But which branch? Is there any branch...
  17. H

    Find the continuous branch cut of a complex logarythm

    Homework Statement Find the continuous branch cut of a complex logarythm for C\[iy:y=>0] One of the complex numbers, for example, is -4i Homework Equations I don´t understand what to do with the subset. How could I find the continuous branch cut in the subset? The Attempt at a...
  18. C

    Which branch of mathematics does arg max come from?

    Homework Statement Which branch of mathematics does arg max come from? The set theory? Homework Equations The Attempt at a Solution Googling
  19. J

    What branch to take: electonics or computer science

    I'm in dilemma over electronics and computer science and engineering. Actually i like everything - everything related to science is interesting to me which adds to my difficulty in choosing the course But i don't know much about - what ill learn in electronics and computers? Do computer...
  20. C

    Which branch of mathematics is this?

    Homework Statement I'm wondering which branch of mathematics is given in the following paper. What I understand in it is the function set mapping notation (f:X->Y), series and sequence notation, but nothing else. I want to know which branch of mathematics this is to be able to read this paper...
  21. P

    Branch Circuits: What is and isn't?

    I'm evaluating an electrical enclosure for a power-plant. Power plants are not required to follow CSA standards, however this electrical enclosure does anyway. Upstream of the enclosure is a rated breaker, and this is what is currently defined as the 'branch.' However, inside of the enclosure...
  22. P

    Complex Analysis - Branch Definition

    Homework Statement Hi everyone, This is more of a definition clarification than a question. I'm just wondering if a branch is the same thing as a branch line/branch cut? I've come across a question set that is asking me to find branches, but I can only find stuff on branch lines/cuts and...
  23. C

    Which branch of mathematics predominates here?

    Homework Statement As the title says, which branch of mathematics predominates in the equation below?Homework Equations Source: http://en.wikibooks.org/wiki/Macroeconomics/Optimal_Growth The Attempt at a Solution I'm not very familiar with the max operator, and don't really know where it...
  24. C

    Which branch of mathematics is this?

    Homework Statement Which branch of mathematics predominates in the equation below? Homework Equations Source: http://en.wikipedia.org/wiki/Taylor_rule The Attempt at a Solution I know that a line over a number can mean either a statistical mean or a complex conjugate, and that...
  25. C

    Which branch of mathematics is this?

    Which branch of mathematics has "max" operators? In which branch of mathematics one would express "biggest real x which satisfies A(x) = B(x)" this way?: max{x ∈ R : A(x) = B(x)}
  26. B

    Branch cut of the principle value log

    Homework Statement Find the branch points of g(z) = log(z(z+1)/(z-1)) and defining a branch of g as the principle branch of the logarithm find the location of the branch cuts. Homework Equations The Attempt at a Solution Since g(z) = log(z) + log(z+1) - log(z-1) the branch points are 0, 1...
  27. J

    Engineering Which branch of engineering will be best in the future?

    Hello, me again, I was told in my last thread "Unsure 10th grader about the future" to invest my energies more towards engineering. That being said, which Engineering branch is going to be better suited in the future? My time frame for graduating, with a B.Sc., is from 2016-2018 (Sophomore in...
  28. B

    Programs What branch of engineering or physics do i have to major in if ?

    I want to be in the research, development and construction of quantum computers, quantum circuits etc? General electrical engineering with a focus on quantum tech or will something along the lines of physicist be enough? Thanks
  29. M

    Principal branch of the logarithm

    Homework Statement Define an analytic branch f(z) of w, such that f(z)=0 for the limit of z->\infty Now what is f(1)? Homework Equations w=\frac{z+i}{z-i} The Attempt at a Solution The branch cut of the logarithm is: (-\infty,0) All branches of the logarithm are...
  30. P

    Physics Becoming a Theoretical or Astronomy-Physicist: High School Prep Advice

    I am planning on be a theoretical physicist or a astonomy-physist, but I need to make sure there's a possible career need for those fields before I choose it. Also I need to know what classes I should take, as I have three more years of high school. So I need to know what classes to start...
  31. L

    Linear Programming - Branch and Bound Method

    Homework Statement I'm trying to learn the Branch and Bound method. For that, I need to master the Dual Simplex Method (DSA). I have tried and tried and tried to google examples but can't find any. Does anyone know where I can find any? How do you know the LPP has become infeasible with...
  32. B

    What branch of mathematics to study to understand Quantum Mechanics?

    I just got a book on Quantum Mechanics, but at a loss with the maths. I had Algebra, Trigo, Calculus, differential equations, etc, but that was a long time ago, now as a programmer, I hardly ever think of those and forgotten them as a result. I believe I still have strong enough concept of...
  33. B

    Tree Branch on Wires: Discuss Strange Arc & Effect

    [url]g4ph-h7l_aM[/youtube] This is pretty old but it just crossed my mind. Wanted to share it with you guys. One question though, why is that current arc going upwards? And why did it appear at all? Can we discuss this effect?
  34. B

    Equivalent Resistance and Branch Currents in Non-simple Circuits

    I'm asked to find an equivalent resistance and the current through each branch of the following circuits. (r is a fixed arbitrary value for all resistors in the circuits) Homework Equations V=IR Sum of I at a node = 0 Sum of V about a closed loop = 0The Attempt at a Solution I've been playing...
  35. R

    "Principal Branch Square Root of z in Domain C-{0}

    Homework Statement Does the principal branch square root of z have a Laurent series expansion in the domain C-{0}? The Attempt at a Solution Well I'm not really sure what a principal branch is? I believe that there is a Laurent series expansion for z^(1/2) in C-{0} because originally our...
  36. M

    Engineering Thévenin resistance when branch is 0V (RC circuit)

    Homework Statement Prior to t=0, switch is in position A (for long time). Afterward, switch is in position B. We need to derive the equation for vc. Homework Equations v(t)=v(\infty)+[v(0)-v(\infty)]e^\frac{-t}{\tau} \tau=RC The Attempt at a Solution at t=0...
  37. S

    Inverse Laplace Transform and Branch Points

    Homework Statement Find the inverse Laplace Transform of \frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1} Homework Equations The complex inversion formula (well known) The Attempt at a Solution The first thing is finding singularities and branch points and so on. From the \frac{1}{s}...
  38. O

    Confusion about solution to contour integral w/ branch pt.

    Homework Statement I am reading the solution the integral of (log(z))^2/(1+z^2) from 0 to infinity in a textbook, and I'm not sure I quite understand it, and I think this misunderstanding stems from my difficulty w/ branch points/cuts for multivalued functions. Homework Equations...
  39. S

    Find Continuity of f_α Along Negative X-Axis

    Homework Statement Find a branch of w=z^{1/2} which is continuous along the negative x-axis. The Attempt at a Solution The book proves that the principle square root function |z|^{1/2} \big( \cos(\theta/2) + i \sin(\theta/2) \big), where -\pi < \theta \leq \pi is discontinuous along the...
  40. 1

    Independent branch of Mathematics?

    I have done well in undergraduate mathematics, and would like to do some self study in something more advanced and stimulating. I am interested in concepts such as number theory and set theory, or any type of mathematics that can be used to study systems of information, behavior...anything...
  41. Z

    [Complex Analysis] Branch cuts of the logarithm

    Homework Statement Consider a branch of \log{z} analytic in the domain created with the branch cut x=−y, x≥0. If, for this branch, \log{1}=-2\pi i, find the following. \log⁡{(\sqrt{3}+i)} Homework Equations \log{z} = \ln{r} + i(\theta + 2k\pi) The Attempt at a Solution This one...
  42. N

    Engineering Need help finding current in a branch within a circuit

    Homework Statement Homework Equations KCL and KVL. V=IR The Attempt at a Solution I tried to combine all the resistors, and I ended up with an equivalent resistance of about .44444 mA. Is my value for equivalent resistance right? Also, does this mean that the resistance passing...
  43. G

    What are the branch points for \log (z^2 + 2z + 3)?

    Hi everyone, Could someone please help me calculate the branch points?
  44. B

    Complex: Defining Sqr(-1) in Main Branch of logz

    Complex: Defining Sqr(-1) using Main Branch Logz Posted: Jul 3, 2011 12:46 PM Plain Text Reply Hi, All: I am having trouble understanding how/if sqr(-1) can be defined when we use the standard branch Logz of logz: As far as I know, we define the complex exponential...
  45. T

    Question about which branch of physics this would be

    Question about which "branch" of physics this would be... I posted this in General since I wasn't sure... and it's not an actual problem, per se, just an inquiry about the fields of physics... (sorry if this is the wrong forum >_>) During work at lunch one day, I was stumbling through...
  46. A

    Engineering Which branch of Engineering involves most theory?

    I aspire to do Engineering at Uni, however I am not quite sure on which field to go into. I much prefer theory and Mathematics to hands on or practical work, I don't mind moderate doses but I would simply prefer a branch that involves more theory and Mathematics etc Im considering Electrical...
  47. T

    Complex Analysis Mapping With Principal Branch

    1. Verify that f(z) = Sqrt(z^2 - 1) maps the upper half plane I am z > 0 onto the upper half plane I am w > 0 slit along the segment from 0 to i. [Hint: use the principal branch] 2. Homework Equations We studied factional linear transformations with T(z) = (a z + b) / (c z + d) , but I...
  48. V

    Excitation of optical branch phonons

    As I studied, the optical branch of a crystal is called so because it can be excited with e.m. fields but I wondered whether it is possible to excite the optical branch also with chargeless particles like neutrons or the charge/action-on-charge is necessary for the process? And if so, why? I...
  49. N

    [complex analysis] are branch points always isolated?

    You can choose to limit yourself to continuous or analytical functions
  50. T

    How do I know it's the positive branch

    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...
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