What is Terms: Definition and 1000 Discussions

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  1. G

    Derivative of a complex function in terms of real and imaginary parts.

    Hi, I wonder if anyone knows when (maybe always?) it is true that, where z=x+iy \text{ and } f : \mathbb{C} \to \mathbb{C} \text{ is expressed as } f=u+iv, \text{ that } f'(z)=\frac{\partial u}{\partial x}+i\frac{\partial v}{\partial x}? I'm pretty sure that this is true for f=exp. I...
  2. M

    An interpretation of quantum mechanics in terms of Brownian–like motion.

    Edward Nelson, a Princeton mathematician showed that quantum mechanics could be derived from the principle that elementary particles are subjected to a universal jiggling of an unspecified cause. As I understand the obstacle to use this mathematical model as a physical one, is that dynamics of...
  3. M

    Giving the Equation of a Line in terms of X, y and theta

    Given an equation for a line y=7x/3, how can i define it in mathematica using x,y and theta. I am eventually going to have to find the intersection of this line to a circle with the equation Circle[{0,9},5] as a function of theta. I thought maybe if i use the rule tan(θ) = y/x then id get...
  4. A

    Ladder of mass M and length L, find kinetic energy in terms

    Homework Statement A ladder of length L and mass M leaning against a wall. Assuming the wall and the floor are frictionless, the ladder will slide down the wall and along the floor intl the left end closes contact with the wall. Before the ladder loses contact with the wall there is one degree...
  5. Pengwuino

    I have agreed to the Terms and Conditions

    "I have agreed to the Terms and Conditions..." Peng here. As I installed Adobe Flash update #15,203,203 and clicked the usual "blahb lah blah terms and crap, don't use Flash to create a nuclear weapon or biological warfare please or we'll sue you", I started wondering how often people ever...
  6. G

    Monotonic 0<an<1 for all n and no two terms are the same

    Homework Statement Give an example of a sequence {an}, satisfying the following: {an} is monotonic 0<an<1 for all n and no two terms are the same lim(n→∞) an = 1/2 Homework Equations what is monotonic The Attempt at a Solution 1/(2√n) n/(2n-1) 1/2^n just been trying...
  7. O

    Second derivative in terms of x and y?

    Homework Statement Find y" in terms of x and y: y^2 + 2y = 2x + 1 Homework Equations N/A The Attempt at a Solution I found the first derivative: y^2 + 2y = 2x + 1 2yy'+2y'=2 2y'.(y+1)=2 y'=2/2(y+1) y'=1/(y+1) But I'm having trouble moving on from there.
  8. Femme_physics

    Algebra - Is it possible to solve it in terms of r?

    I appear to be getting two sides with the same unknown. Does it mean I'm screwed and can't solve it in terms of "r"? http://img716.imageshack.us/img716/4409/image2011121500032.jpg
  9. M

    Writing a sequence in terms of n.

    Homework Statement given: Vn+1=Vn*cos(pi/2^(n+2)) Homework Equations Write a sequence Vn in terms of n The Attempt at a Solution we substitute n with n-1 and we get: V(n-1)+1= Vn-1*cos(pi/2^(n-1+2)) Vn=Vn-1*cos(pi/2^(n+1) Is this correct?
  10. A

    Could someone me solve for ε in terms of [itex]\delta[/itex] ?

    As part of my problem I need the following condition to hold: \frac{2^{n(H+\epsilon)}}{\epsilon}:=\delta^{-\theta} for some \epsilon, \delta and \theta all in (0,1). Now, I would like to rearrange the equation (solve for \epsilon[itex/] in terms of the rest of the parameters) so as to have the...
  11. J

    Mathematica [Mathematica] Sorting polynomial terms

    Hi. Can someone explain to me how to sort a Series so that the terms are in increasing powers of the exponent? For example the code: myseries = Normal[ Series[Sqrt[1 - w], {w, 0, 5}]] /. w -> 1/z produces 1-\frac{7}{256 z^5}-\frac{5}{128 z^4}-\frac{1}{16 z^3}-\frac{1}{8 z^2}-\frac{1}{2...
  12. W

    Need an explanation of shells in layman's terms

    We just did atomic physics in class, and my teacher assumed everyone had already taken chemistry so she really skimmed through the material, and I have yet to take chemistry so I am beyond lost with this chapter. I read the chapter and it is so technically written that I don't comprehend it...
  13. Z

    Bernoulli equation in terms of energy per unit volume

    dear PF.. what is the Bernoulli equation in terms of energy per unit volume the equation include the 1) static pressure 2) hydrostatic pressure 3) dynamic pressure 4) stagnation pressure
  14. M

    Write as a simple fraction in lowest terms

    Homework Statement \frac{\frac{2}{3}x(x^{2}+4)^{1/2}(x^{2}-9)^{-2/3}-x(x^{2}-9)^{1/3}(x^{2}+4)^{-1/2}}{x^{2}+4} The Attempt at a Solution \frac{x(x^{2}+4)^{-1/2}(x^{2}-9)^{-2/3}(\frac{2}{3}(x^{2}+4)-(x-9))}{x^{2}+4} Then: \frac{x(\frac{2}{3}(x^{2}+4)-(x-9))}{(x^{2}+4)^{3/2}(x^{2}-9)^{2/3}}...
  15. J

    Understanding Rest, Stillness, Stationarity, Motion, Movement, and Travel

    This may seem obvious, but please define these for me, in as much details as possible. What does it mean to: "be at rest" "be still" "be stationary" "to be in motion" "to move" "to travel" Please do so without using one of the words in another one's definition (I.e. stationary means...
  16. T

    Summing n-number of Terms to Find the Area of a Polygon

    Homework Statement Let C be the line segment connecting the points (x1,y1) and (x2,y2). More over let the line integral over C of (x dy - y dx) = x1y2 - x2y1. Suppose the vertices of a polygon, listed in counter-clockwise order, are (x1y1), (x2y2), ... , (xnyn). Show that the area of the...
  17. P

    Analysis: Absolute convergence, rearranging terms, power series question

    Homework Statement I can't figure out what my professor means in the last two lines: I'm trying to prove why the product of two analytic functions is analytic, and I think that I am going to need to use a similar construction. The Attempt at a Solution So far to prove the product...
  18. X

    Characterizing transitive G-set actions in terms of orbits

    Homework Statement A group G acts transitively on a non empty G-set S if, for all s1, s2 in S, there exists an element G in G such that g*s1 = s2. Characterize transitive G-set actions in terms of orbits. Prove your answer Homework Equations Transitive G-set Actions: for all s1, s2 in S...
  19. 1

    Finding the First 4 Nonzero Terms of e^tcos(t)

    Homework Statement Find the first 4 nonzero terms of: e^{t}cos(t) Homework Equations The Attempt at a Solution I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently. Should I list 4 terms of each series, then...
  20. S

    Geometry Fields in Laymens Terms

    The concept of describing something in layman's terms has come into wide use in the English speaking world. To put something in layman's terms is to describe a complex or technical issue using words and terms that the average individual (someone without professional training in the subject area)...
  21. M

    What is the definition of greater than or less than in terms of real numbers?

    A thought just struck me today after watching a lecture on the construction of the rational numbers. What is the definition of 'greater than (>)' and 'less than (<)' in the real number system. The only way I can think to describe it is to make some reference to the Euclidean distance between the...
  22. K

    How many terms of the series are needed in order to estimate the exact sum within .01

    Homework Statement How many terms of the series ∞ Ʃ (-1)n/(ln(n+1)) n=1 are needed in order to estimate the exact sum within .01 Homework Equations I know that I need to use the remainder estimate for the integral test where Rn=s-sn and that ∫ from (n+1) to ∞ of f(x)dx \leq Rn...
  23. E

    Find h in terms of angle with the vertical (rotational KE)

    Homework Statement "A rod of mass 4.0 kg and length 1.5 m hangs from a hinge. The end of the rod is then given a 'kick' so that it is moving at a speed of 5 m/s. How high will the rod swing? Express you answer in terms of the angle the rod makes with the vertical.Homework Equations KE(rot) =...
  24. B

    Obtain an expression for the expectation value in terms of energy

    Homework Statement The ground state wave function for a particle of mass m moving with energy E in a one-dimensional harmonic oscillator potential with classical frequency omega is: u(subscript 0) (x)= N(subscript 0) exp((-alpha^2)(x^2)/2) and alpha=sqrt (m *omega/h-bar) where...
  25. R

    Simplifying Polynomial: (1/(2s+3))

    Homework Statement I'm trying to simplify this polynomial ((s+1)/(2+s))/((s+1)+((s+1)/(s+2))(s+1)) It's more readable if you view it here: http://www.wolframalpha.com/input/?i=%28%28s%2B1%29%2F%282%2Bs%29%29%2F%28%28s%2B1%29%2B%28%28s%2B1%29%2F%28s%2B2%29%29%28s%2B1%29%29 It simplifies...
  26. V

    Vectors, velocity in terms of unit vectors

    Homework Statement A particle moving in xy plane has velocity components in x and y directions Dx/dt = b1+c1t and dy/dt = b2+c2t A) integrate above equations to give displacement components x and y as functions of time B) write the velocity (v) of the particle at time t in terms of...
  27. F

    Source Terms Explained: Fluid Dynamics for Newbies

    I'm relatively knew to fluid dynamics. I'm self teaching myself. Could someone explain what it means to say a function or vector is a source term? Are there any significant mathematical properties/uniqueness's? I'm working with vector matrices, so if you could explain in this context that...
  28. K

    What is the simplest way of selecting the last N terms of a polynomial?

    If you have a polynomial like (1+x)^6 = x^6+6 x^5+15 x^4+20 x^3+15 x^2+6 x+1, What function would you use to pick only the last N terms? For instance, for N=3 pick x^6+6 x^5+15 x^4 I've being using sum of a binomial times something, but was wondering if there is anything more simple. Thanks!
  29. A

    Mathematica Defining one matrix in terms of another in Mathematica with FOR loop

    THIS ISN'T WORKING AT ALL! I'm trying to define a matrix M in terms of a predefined matrix N by using the following for loop: For[a=1,a<=12,a++,M[[a,a]]=N[[1,a]]] So I just want the diagonal of M to be the first row of N. But this is not working at ALL. Does anyone see what I'm doing wrong?
  30. G

    Calculus 2 - Infinite Series Question - Estimating Series with Positive Terms

    Homework Statement Consider the following convergent series. Then complete parts a throw d below. sum[k=1,inf] 5/k^7 a. Find an upper bound for the remainder in terms of n Homework Equations Estimating Series with Positive Terms Let f be a continuous, positive, decreasing...
  31. I

    Solve Non-Linear DEs w/ Many Consts Using Mathematica

    How can a system of non-linear differential equations be solved using Mathematica? More specifically, I understand the process that needs to be executed, but I don't understand how to make it work syntactically. The process as I understand it: Four expressions are given in four...
  32. S

    Linear Algebra: Solve B^(-1) with A, C, D

    I'm looking for help to this problem. Here is my attempt: I being the identity matrix and B^(-1) being B to the negative 1st power. A (B B^(-1)) C D = B^(-1) I so A I C D = B^(-1) so A C D = B^(-1) Thank you for any help.
  33. F

    Solving Implicit Equations for y in Terms of x

    How do you go about solving implicit equations for y in terms of x that look like these? y2 + yx = 1 and y3 + yx = 1 or even more complicated implicit equations. I'm taking AP Calculus AB this year and am just curious how this is done. Here are the solutions from Wolframalpha...
  34. E

    How Can We Validate Equating Terms in Infinite Summations?

    Today my physics professor briefly skipped over this during a derivation: We started with 2 \sum F_{n}(x) = \sum G_{n}(x) , summed from n=0 to \infty which she then concluded 2F_{n}(x) = G_{n}(x) where F and G are functions of x, and different functions for different values of n...
  35. W

    Recursive sequence terms don't cancel

    Homework Statement The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum Sn. Homework Equations The Attempt at a Solution 3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)...
  36. A

    Rewriting the fourth moment in terms of

    rewriting the fourth moment in terms of... Homework Statement X is a random variable with moments E[X], E[X^2], E[X^3]. Suppose var(X)= σ^2, and that skewness is given as, S=[E(X-μ)^3)]/(σ^3) Rewrite the right hand side of the expression(see below) in terms of μ, σ^2, S and μ4 Homework...
  37. G

    Energy of an damped/undriven oscillator in terms of time?

    Homework Statement The Q asks to show that the time rate of change in mechanical energy for a damped, undriven oscillator is dE/dt=-bV^2.Homework Equations I assume you take the derivative of the total E eq, E=(1/2)mV^2 + (1/2)kx^2 but I'm unsure how to put the E eq into terms of t, like...
  38. T

    Mathematica Mathematica: Splitting a function into a list of terms

    Hi, I need to split an expression into a list of terms, i.e. an expression like: a+b-c-d+... into: {a,b,-c,-d,...}. Can you help? Thanks in advance.
  39. T

    Specific technical definitions of quantum terms

    I feel that a lot of the misunderstaing in quantum physics arises from the misinterpretations of terms used by physicists. I think that the forum should have a page where all the quantum terms are explained in a precise technical manner to avoid confusion. I will state pop culture's...
  40. T

    Zeroth law of thermodynamics in terms of heat

    Is there any definition of the zeroth law of termodynamics using the heat concept? And does the zeroth law imply that the only way 2 systems can transfer energy is if they're not in thermal equilibrium? If 1 system is transferring energy to another one, that means they're not in thermal...
  41. L

    Splitting up exponential terms when integrating

    1. Relevant problem integrate from 0 to infinity of r^2exp^(-r/a0)dr Homework Equations I'm also given; integral from 0 to infinity of x^nexp^-x dx = n! The Attempt at a Solution I'm just wondering if I can split up the exponential to make it look like this form. Eg; integrate from 0 to...
  42. DryRun

    N(A) and R(A) in terms of their basis

    Homework Statement The matrix A = 1 1 1 1 -1 0 1 0 1 2 3 2 Express null space and row space of A in terms of their basis vectors. 2. The attempt at a solution I have found the null space to be: x3 [1 -2 1 0]^T + x4 [0 -1 0 1]^T. But my problem is how do i write the final answer correctly...
  43. M

    Higher order terms of Range Kutta for SPH?

    I am using smooth-particle hydrodymamics(SPH) method to model a deformable object. It is based on the procedure found in Markus Gross's point based animation book, the algorithm is attached in the image below. This algorithm uses Euler for numerical integration as seen in step 21 and 22, and...
  44. I

    Can someone explain polarization states to me in really simple terms?

    Let's say I have an equation E=iE0cos(kz-wt)-jE0cos(kz-wt), how do I look at this and know, this is linearly polarized? or what if it changes and the kz is negative? or its a sin function with with (wt-kz-pi/4) in it. I just don't understand what this equation is supposed to be telling me and...
  45. A

    Planning the year in terms of Research

    So I'm a second year Physics and Math major with the long term goal of a PhD in Theoretical Physics or maybe Math. I asked around at the start of this semester whether there was anything available for me in terms of research in the Physics department. I found a professor willing to take me on...
  46. M

    Starting initial value problems when terms are expressed only in x

    How should I go about starting the following two problems solve the following initial value problems x''-4x=0 ; x(0)=1, x'(0)=0 and x''-4x'+4x=0 ; x(0)=1, x'(0)=0 Should i use a general solution with the basis m^2-4=0 for problem one and m^2-4x+4=0 for the second?
  47. L

    Integrating double exponential terms in a function

    Hi, this is not really a homework problem, but something that came up during my research, upon trying to integrate some empirical function. This function consists of many terms, but specifically, there is a term containing double exponential functions which is giving me some trouble. If...
  48. R

    Classical mechanics - finding distance D in terms of velocity

    Homework Statement "A passenger (mass m) initially at rest steps out of an airplane. Assume down is the positive x-axis and put the origin at the airplane. Assume the air resistance force is linear in the velocity so F(air)= -mbv. Find the distance D he has fallen when his velocity is...
  49. V

    Evaluting Summation of Mutiplied Terms

    Homework Statement Evaluate the sums: \sum^{n}_{i=1}ia^{i} Homework Equations The Attempt at a Solution I'm assuming that because there's no limit or anything, the professor wants an equation. I know \sum^{n}_{i=1}i is \frac{1}{2}n(n+1) and \sum^{n}_{i=1}a^{i} is \frac{a^{n+1} - 1}{a-1}-1...
  50. W

    Second Derivative in Terms of Y

    Homework Statement Find the second derivative of 4x^2 + 3x - 9y^2. Answer in terms of y. Homework Equations All derivative formulas. The Attempt at a Solution [PLAIN]http://http://i52.tinypic.com/2w2ptex.jpg I can't get much further than this; the thing that gets me is how to put...
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