What is Terms: Definition and 1000 Discussions

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  1. R

    Missing h-bar in showing SHO in terms of ANHIL and CREA operators is correct

    this is the given: the problem is the middle term, if the h-bar w outside the set brackets is canceled with the h-bar w of the m/2hw, then there will be a h-bar w that is left introduced from the middle term, i.e. i\frac{w}{m}XP- i\frac{w}{m}PX = i\frac{w}{m}[X,P]= i\frac{w}{m}i\hbar but...
  2. L

    MHB Creating terms that have the value 0

    Hey, I just found this interesting exercise and I'd like to know how to solve it. The exercise: Between the numbers 4, 5, 6, ... , n, you can put minus or plus signs ( - , +) to create a term. (n means any natural number) and (the numbers must be in order) Which possible numbers for n can...
  3. H

    Real gas equation in terms of Cv?

    Is there a form of the van der waal equation in terms of the Cv of the gas? Is it derivable?
  4. M

    How Is Gravitational Acceleration Expressed Using Distance and Time Intervals?

    Homework Statement In a physics laboratory the value of g, the gravitational acceleration in the vicinity of earth, has been measured accurately by projecting a ball up an evacuated tube and electronically timing the passage of the ball in its upward and downward flight through two light...
  5. B

    Interpretation of induction in terms of symmetry transformations

    It just occurred to me that induction can be seen as a statement quite analogous to that of "a function whose derivative is 0 on an interval is constant on that interval". Suppose there is a property P about the natural numbers that we want to prove. Then let P: N -> {0, 1} be a function for...
  6. E

    Simple Definition of a "Math Restriction" (Layman's Terms)?

    Homework Statement For which value(s) of x is each expression not defined? Homework Equations x^2+3x-6 divided by x^2-x-12 The Attempt at a Solution The answer that was given turned out to be: x^2+3x-6 divided by (-4)(x+3) Restrictions: x ≠ 4,-3...
  7. H

    MHB Simplifying by combining terms

    Ok.. What about this one? \frac{1}{y+1}+\frac{2}{x+2}+\frac{\frac{x+2}{y+1}-2}{x+2} this is where I am at: \left(\frac{x+2}{y+1}-2\right)
  8. O

    MHB Can a polynomial ever just have 2 terms?

    Or does it always have to have MORE THAN 2 like x^2 +x^2 -4a polynomial can never be x^2 - x-^3 Right?
  9. KleZMeR

    Cauchy - Riemann Function in terms of Z

    Homework Statement I found the function V, which is the conjugate harmonic function for U(x,y)=sin(x)cosh(y). I am attaching my work. It turns out to be a two-term function with trig factors. I am then to write F(Z) in terms of Z, but is plugging in x, and y, in terms of Z into my trig...
  10. Telemachus

    Continuum mechanics, physical interpretation of terms in balance eq.

    Hi there. I'm reading Gurtin's 'the mechanics and thermodynamics of continua', and working some exercises of his book. In the section 21: 'The first law: balance of energy', after the derivation of the balance equation, he uses an identity to rewrite the balance of energy. The balance of energy...
  11. F

    Need help understanding these terms

    Need yout help in understanding these terms Hello everyone, nice to meet you all First of all, please know that English is not my mother language and I work as a translator in training and I have these tools and accessories and I really need to know what they do, could you kindly describe what...
  12. K

    Glashow-Weinberg-Salam problem with mass terms

    At the end of spontaneous symmetry breaking I get these mass terms: W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp W_{\mu}^{2} \bigr ) \mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{+}{W^{\mu}}^{-} + \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+} So I have...
  13. C

    Express signal in terms of ramp, exponential, and parabolic functions

    Homework Statement Express the following signal in terms of ramp, exponential, and parabolic functions, where t should be consistently shifted Homework Equations signal simplification techniques, not known to me The Attempt at a Solution It seems you can express this in terms of...
  14. J

    Second Law of Thermodynamics in Terms of Electromagnetic Principles?

    In Heaviside's Electromagnetic Theory (1895) he says that "The second law of thermodynamics itself needs to be established from electromagnetic principles, assisted by the law of averages..." I attempted to Google whether or not anyone has derived the second law via electricity and magnetism...
  15. A

    MHB How can I express f(z) in terms of z using exponentials?

    Hello! I am stuck at the final step. How do I get x+iy from the equation? Help! I am so sorry for posting this question in a picture instead of writing it out, because I don't know how to write equations on here.
  16. M

    How can I express f(z) in terms of z?

    Hello! I am stuck at the final step. How do I get x+iy from the equation? Help! I am so sorry for posting this question in a picture instead of writing it out, because I don't know how to write equations on here.
  17. I

    MHB Finding Surface Area from Equation in Terms of x=g(y)

    if I am finding the surface area, and I am given the equation in term of x=g(y) about the x-axis, do i have to solve for y or can i just integrate in terms of y? would i just use dx/dy instead?
  18. B

    Finding delta in terms of epsilon-delta definition

    Homework Statement If f(x) = 3x+1 en assume δ > 0. Assume ε>0. Give a δ > 0 with the following property : |x-1|< δ => |f(x) - f(1)| < ε Homework Equations The Attempt at a Solution |f(x) - f(1)| < ε <=> |3x+1-(3*1+1)| < ε <=> |3x-3| < ε <=>...
  19. L

    Functioning of AC current in simple terms?

    Hi, Thank you for reading this. I understand the functioning of DC current. You create a potential difference and the electrons flow from the power source through the electrical appliance (thereby, powering it) and flows back, completing the circuit. But, in AC, the electrons...
  20. J

    Another vector fields in terms of circulation and flux

    Other laws in terms of circulation and flux Why others vector fields no are studied like the magnetic and electric fields? In other words, why others vector fields, like the gravitational and the hydrodynamic, haven't "supreme laws" based in the circulation/flux or curl/divergence?
  21. D

    Mathematica Collecting terms in mathematica

    I have an integrand with a handful of terms, and some of them have poles in the denominator of the form (x+c) (but not all). There are three poles in total, and I want to collect all the terms according to each pole individually (eg all the terms with (x-1) in the denominator, (x-5), etc.)...
  22. Govind_Balaji

    Prove a complex expression = 1, if log of the complex terms are equal

    Homework Statement If \frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}, prove that x^{b+c-a}.y^{c+a-b}.z^{a+b-c}=1Homework Equations The Attempt at a Solution I solved a question similar to it in a way. So I tried this in the same way. The only difference between the two questions is...
  23. J

    Can the trace be expressed in terms of the determinant?

    Browsing in the wiki, I found those formulas: http://en.wikipedia.org/wiki/Determinant#Relation_to_eigenvalues_and_trace So, my doubt is: if is possible to express the determinant in terms of the trace, thus is possible to express the trace in terms of the determinant too?
  24. J

    How write a matrix in terms of determinant and trace?

    Given the following: $$\\ \begin{bmatrix} A & 0\\ 0 & B\\ \end{bmatrix}$$ the eigenvalues is exactaly A and B. So analogously, is possible to write a matrix with only two elements, T and D, such that the trace is T and the determinant is D? I tried something: $$\\ \text{tr} \left(...
  25. S

    Write sin in terms of Hermite polynomials

    Homework Statement Write ##sin(ax)## for ##a \in \mathbb{R}##. (Use generating function for appropriate ##z##) Homework Equations ##e^{2xz-z^2}=\sum _{n=0}^{\infty }\frac{H_n(x)}{n!}z^n## The Attempt at a Solution No idea what to do. My idea was that since...
  26. J

    Neglecting High-Order Terms in R: Tips & Tricks

    Hi, Is there a better way to write this? 'terms of order O(R^{-Y}) where Y>1 are neglected' I feel like this is a bit clumsy. Thanks for the help!
  27. E

    "Special" and "General" relativity- Who invented those terms?

    Hi all, I can't seem to find any historic account of when those two theories got their (quite strange) names. Can someone point me to a source? One of the reasons I am interested in this is the persistent idea in popularizing texts, especially from the 1970's, that Special Relativity could...
  28. J

    Can a 2nd Order Linear ODE Be Expressed in Terms of σ and ω?

    If a 2nd order linear ODE: can written in terms of natural frequency ω0 and damping ratio ζ: being: So, it too can be written in terms of exponential decay/growth σ and angular frequency ω?
  29. W

    What are the independent terms in the Magnetic Tensor

    I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...
  30. C

    Rotation and translation of basis to remove cross terms

    So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...
  31. D

    Differential equation substituition of new terms

    Homework Statement for this question, i sub u=xy and try to eliminate y in my working.. but how should i proceed since the term ux cannot be separated Homework Equations The Attempt at a Solution
  32. J

    Can the sinh and cosh functions be expressed in terms of each other?

    Is possible express the sine in terms of cosine and vice-versa: ##\sin(x) = \cos(x-\frac{\pi}{2})## ##\cos(x) = \sin(x+\frac{\pi}{2})## So, of some way, is possible express the sinh in terms of cosh too and vice-versa?
  33. F

    Integral with exponential terms?

    I am doing some analysis and I have come up with the following integral: \int \frac{e^{-ax}}{1+be^{-cx}}dx where a>0, b>0 and c>0. I have found out this integral has a solution in terms of the Gaussian hypergeometric function http://en.wikipedia.org/wiki/Hypergeometric_function but it...
  34. L

    Find the sum of the first n terms

    Homework Statement Find the sum of the first n terms of the sequence U1, U2, U3... Ur Homework Equations The Attempt at a Solution $$ \sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n $$ But I don't this is right... any help?
  35. B

    Derivation of r (radius) in terms of f (frequency)? Help please.

    Okay, so the job I need to do is derive an equation for the radius of an object in terms of its frequency. These are the equations that we are allowed to use: v(Linear velocity) = rω v=2πr/T ω (angular velocity)=2πf f (frequency)= 1/T (time period) T= 2πr/v a (centripetal...
  36. L

    What is the formula for finding the sum to n terms in a geometric series?

    Homework Statement Wn = 2 + 3(1/2)^n Homework Equations The Attempt at a Solution I am confused, all I tried so far is writing out the first 5 terms, but all that was helping me to do is basically find the Sum to infinity... so what should I do to find the Sum to n terms? I know...
  37. nomadreid

    Defn. of information transfer in terms of fields

    I am attempting to get a good definition of the word "information", as in "information can be transferred at most at the speed of light".) Here is my attempt so far. Please indicate if this seems adequate. Starting from the definition in information theory: Given a probability...
  38. A

    MHB How to approximate IRR with simple formula for two loans of different terms

    I am trying to make a simple formula to approximate the IRR using the IRR of each loan, their respective term and loan size. i.e. loan one is $\$1,000,$ has a term of $10$ years and an IRR of $5\%$. loan two is $\$100$ has a term of $1$ year and an IRR of $15\%$. Using a simple weighted...
  39. Y

    Finding the tension in terms of mg

    Homework Statement Attached the question. Homework Equations (total) tension = mg The Attempt at a Solution I'm not sure how the tension gets divided here. I know the tension on the right hand side of the turnbuckle is the same tension on the left hand side since they are...
  40. S

    Summation of 'n' terms of the given expression

    Homework Statement find the general formula to calculate the sum Homework Equations 1+11+111+1111+11111+....upto n terms The Attempt at a Solution 100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ... ==> (100+100+100+...upto n terms) + (101+101+101+...upto n-1 terms)...
  41. M

    MHB P divides all the coefficients of the terms with degree <8

    Hey! :o $f(x)=\sum_{i=0}^{7}{a_ix^i}, g(x)=\sum_{i=0}^{5}{b_ix^i}$, $a_i, b_i$ are integer coefficients. The prime $p$ divides $a_0, a_1, a_2, a_3, a_4$ but it does not divide $a_5, a_6, a_7$. $p$ divides also $b_0, b_1, b_2$, but it does not divide $b_3, b_4, b_5$. $h(x)=f(x)g(x)$ Show that at...
  42. J

    What is the difference between these types of differential equations?

    Which the difference between diff equations of kind: \frac{dy}{dx} = \exp(x) \frac{dy}{dx} = 1/x and diff equations of kind: \frac{dy}{dx} = y \frac{dy}{dx} = \frac{1}{\exp(y)} ?
  43. W

    What are independent terms in Magnetic Tensor

    I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...
  44. nomadreid

    Velocity in Proper Time: Relativistic Acceleration Equation

    Two questions, based on the same situation: in http://physics.stackexchange.com/questions/34204/relativistic-acceleration-equation (question A) it is mentioned that, for an object with a constant acceleration g_{M}, and with \tau_{0} =1/g_{M} , after proper time \tau, the coordinates are...
  45. S

    Finding second derivative of sin y+cos y=x in terms of x

    Homework Statement Find the second derivative of sin y+cos y=x, giving your answer in terms of x. Homework Equations Implicit derivatives The Attempt at a Solution ##\sin y+\cos y=x## ##\cos y \frac{dy}{dx} -\sin y \frac{dy}{dx}=1## ##\frac{dy}{dx}=\frac{1}{\cos y-\sin y}##...
  46. Y

    MHB Solve Recurrence Relation w/ 3 Terms & Initial Conditions

    How to solve this question. Please explain step by step.
  47. S

    Density terms in the stress-energy momentum tensor

    The stress energy momentum tensor of the Einstein field equations contains multiple density terms such as the energy density and the momentum density. I know how to calculate relativistic energy and momentum, but none of the websites or videos that I have watched make mention of any division of...
  48. M

    Doppler Effect inconsistent in terms of relative velocities

    Hi all! Let me use an example to make this clear. There is a car traveling directly toward a man at 10m/s. The car is pressing down its horn, producing a frequency of 100hz. The speed of sound is 330 m/s. What frequency does the man hear? Ok, so we can use the equation: f_observer=(...
  49. R

    Hamiltons equations of motion in terms of poisson bracket

    In Hamiltonian formulation there is an expression df / dt = { f , H } + ∂f / ∂t where f is function of q, p and t. While expressing Hamiltons equations of motion in terms of Poisson Bracket, i.e if the function f = q of p then its partial time derivative ∂f / ∂t becomes zero.. Please explain why?
  50. Ryan_m_b

    Terms physicists and biologists use differently

    I'm giving a presentation to a group next week made up of mathematicians, physicists and mechanical engineers. My talk is going to be related to my work so it's going to be very biology based. I want to start the talk pointing out that life science and the physical sciences are very different in...
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