What is Parameters: Definition and 534 Discussions

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, electronic musical composition.
In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'.

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  1. G

    ODE: Combining Undetermined Coeff. & VOP Method

    Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...
  2. J

    Question about the def. of solving 2nd order ODEs through Var. of Parameters.

    Ok, so I've been studying the method of variation of parameters in order to solve 2nd order ODEs, and I have a question regarding a supposition that is made in the definition of the method. Say, y'' + p(t)y' + q(t)y = g(t) Then the general solution to the above equation is c_1y_1(t) +...
  3. C

    ODE using variation of parameters

    Homework Statement You are given that two solutions to the homogeneous Euler-Cauchy equation x^2 \frac{d^2}{dx^2}y(x) - 5x \frac{d}{dx} y(x) + 5y(x) = 0 y1=x, y2=x^5 y''-\frac{5}{x}y'+\frac{5}{x^2}y=-\frac{49}{x^4} changing the equation to standard form use variation of parameters to find a...
  4. H

    Calculate Parameters of Shifted Exponential Density from Measurements

    I have a density function: f(t) = L * e-L(t-t0) * u(t-t0) where u(t) is the unit step function. And I have a column vector X, which is randomly chosen samples from f(t): X = [x1 x2 ... xn]T How can I estimate the unknown values t0 and L from this X vector?
  5. B

    Differential Equations: Variation of Parameters

    Homework Statement Find the particular solution to the differential equation using method of variation of parameters: 4y''-4y'+y=16e^(t/2) The Attempt at a Solution Set 4y''-4y'+y=0 then the homogeneous solution is: y= c1*e^(t/2)+c2*te(t/2) set y1= e^(t/2), y2= te^(t/2)...
  6. E

    Understanding Earth Parameters: Dip Angle, Latitude & More

    Hi All, I have some parameters here and I can not understand what are they mean? dip Angle dip Latitude invariant Latitude Geomagnetic Latitude L-Shells Thanks
  7. F

    Calculating Circular Polar Orbit Parameters and Fractional Doppler Shift

    Hii guys.I have this problem.Can anybody help me on this.tq Homework Statement A satellite is in a circular polar orbit at a height of 870 km, the orbital period being approximately 102 min. The satellite orbit passes directly over a beacon at sea level. Assuming an average value of...
  8. B

    Orbit Energy and Eccentricity Derivation

    Homework Statement Ok so take r' to be r dot.. i have E = 1/2m (r' ^2 + h^2/r^2) - A/r = E Energy equation for central force (inverse square) and r = l/(1+ecostheta) where l is the latus rectum.. need to derive the expression linking E and e i.e. E= A^2/2mh^2 (e^2-1) but can't...
  9. P

    Using kinetic and dynamic principles to determine unknown parameters

    A motor vehicle has a mass of 700Kg and is traveling at 36 km/h on a level road; it is taken out of gear and allowed to roll to a stop. The first part of the question asks me to work out the kinetic energy which I've done and then the next part asks how far will it travel if the rolling...
  10. Y

    Question on Variation of Parameters

    I have a question on the integration part of the Variation of Parameters. Given .y''+P(x)y'+Q(x)y=f(x) The associate homogeneous solution . y_c=c_1y_1 + c_2y_2. The particular solution . y_p=u_1y_1 + c_2y_2. u'_1 = -\frac{W_1}{W} = -\frac{y_2f(x)}{W} This is where I have question...
  11. L

    Variation of Parameters, system of equations

    Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...
  12. A

    Eliminate Parameters to Find Ellipsoid Cartesian Equation

    Homework Statement Eliminate the parameters u and v to obtain a Cartesian equation, thus showing that the given vector equation represents a portion of the surface named. Also, compute the fundamental vector product dr/du x dr/dv in terms of u and v.Homework EquationsEllipsoid r(u,v) =...
  13. E

    How measureable parameters associate with operators

    Homework Statement in quantum mechanics, if we have a wave function, and an operator, we can know the eigenvalue from the eigen equation:\hat{F}\phi=f\phi. but how we obtain the mathematical form of operator \hat{F}? Homework Equations \hat{x} \rightarrow x ? \hat{p} \rightarrow -ih...
  14. J

    Engineering Materials - Ramberg Osgood Parameters Help

    I am currently doing a material characterisation project and have performed a standard tensile test on a number of 304 stainless steel specimens. I have obtained a number of stress-strain curves from the testing and have been told I need to relate them to the Ramberg-Osgood material model in...
  15. A

    Is it possible to calculate hour-glass parameters using calculus?

    Is it possible to calculate "hour-glass" parameters using calculus? The standard hour-glass model drops sand from the top cone to the bottom in an hour. Is it possible to calculate the mass of sand that would be required for making an hourglass? Further, would it be possible to change the...
  16. J

    Engineering Materials - Ramberg Osgood Parameters Help

    I am currently doing a material characterisation project and have performed a standard tensile test on a number of 304 stainless steel specimens. I have obtained a number of stress-strain curves from the testing and have been told I need to relate them to the Ramberg-Osgood material model in...
  17. B

    MATLAB Using ode45 in a for Cycle: Adding Parameters to odefun

    Hi guys, I want to run a for cycle with ode45 inside. However, some parameters that I define in odefun (the differential equation in order to dy/dt, for instance) assume different values in each iteration of that cycle. I find help examples showing odefun only receiving t and y... Is...
  18. M

    Differential equations, variation of parameters

    Homework Statement Using variation of parameters, find the general solutions of the differential equation Homework Equations y''' - 3''y + 3y' - y = et / t where et/t = g(t) The Attempt at a Solution I know how to solve these types of equations when its a second order, but I don't...
  19. P

    Where to get UNIFAC Parameters Table?

    Hello..I am looking for UNIFAC-VLE Subgroup Parameters Table online but can't find any..where can I get it? By the way..how should I categorize C=C compound for example butene and compound like dimethylformamide when using UNIFAC VLE method? Thanks for helping...
  20. O

    Uncertainty in parameters -> Gauss-Newton

    Uncertainty in parameters --> Gauss-Newton Hi guys! I have a set of datapoints, and i´m about to use Gauss-Newton to fit a model function (Lorentzian) to these points. So we´re talking abut a nonlinear least squares regression. How do I estimate error in function parameters given errors...
  21. N

    How to calculate lattice parameters?

    Dear Friends, I read some articles about alloys. Most articles have a table listing lattice parameters (a,b,c-axis) and unit cell volumes. But they never explain how those data come from. How do we get those data? By comparing XRD images with PDF databases? Or by calculation? Example...
  22. I

    Learning H Parameters of Transistors: A Guide to Electronics Books

    can someone recommend me a good electronics book to learn about h parameters of transistors
  23. cepheid

    Variation of Density Parameters with Redshift

    I was looking at section 7.6 of Longair's Galaxy Formation, and in it, he is talking about the flatness problem, or fine-tuning problem. In it, he shows that if you define a general (i.e. varies with cosmic time and hence with redshift) density parameter \Omega_m for matter by analogy with...
  24. H

    Solving EM Problem with Variation of Parameters

    I am trying to solve the following equation using the variation of parameters method d2x/dt2-(q2Bz2/m2)x=qEx/m I have put x1=cos(t) and x2=sin(t) into the Wronskian method. Can someone tell me if these are the correct functions to use, or should I be using exponential functions. Any...
  25. L

    Solving ODE for Sinusoidal Voltage: Current i in Terms of Parameters and t

    setting a sinusoidal voltage term, the ODE can be written as (d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt) assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are i(0) = di/dt (0) = 0 i really don't have much of...
  26. S

    Problem in setting homogenous parameters

    Homework Statement how to put x+z=0, and y-z+2w=0 into matrices in terms of two parameters? Homework Equations AX=0, looking for x The Attempt at a Solution x=-z y=z-2w (-1, 1, 1, 0)z, no idea what the other matrix is :S thanks advance guys!
  27. E

    Variation of Parameters (Diffy Equ.)

    Homework Statement t²y"-t(t+2)y'+(t+2)y= 2t³ y1(t)=t y2(t)=te^t t>0 Homework Equations w(t)=y1*y2' - y1*y2 g=2t y=-y1∫(gy2)/w + y2∫(gy1)/w The Attempt at a Solution y1=t y1'=1 y2=te^t y2'=e^(t)+ te^(t) w(t)=te^(t)+t²e^(t)-te^(t)=t²e(t)...
  28. A

    Variation of parameters (Kinda having trouble with the integral)

    Homework Statement Solve the problem: 4y'' - y = 8e^(.5t)/(2 + e^(.5t)) Homework Equations Particular solution of Y = X*integral(inverse of X multiplied by G) Finding eigenvalues and eigenvectors The Attempt at a Solution This might be a little too messy for anyone to make...
  29. R

    Solving Linear Systems Using Variation of Parameters

    Homework Statement (x2+1)y"+(2-x2)-(2+x)y=x(x+1)2 given 2 associated homogeneous solution are: ex and 1/x Homework Equations this is a question from shaum's outline differential equations chapter on "variation of parameters"The Attempt at a Solution so here what i got... yh=C1ex+C2(1/x)...
  30. J

    Finding a particular solution for y''+4y=20sec(2t)

    Homework Statement Find a particular solution to: y''+4y=20sec(2t) Homework Equations The Attempt at a Solution y''+4y=0 r^2+4=0 r=+or- 2i So, yc(t) = Asin(2t) + Bcos(2t) yp(t)= -cos(2t) ∫ 10sin(2t)sec(2t)dt + sin(2t) ∫ 10cos(2t)sec(2t)dt = -10cos(2t) ∫...
  31. D

    Scattering Matrix parameters: Conceptual questions

    First off, this is not a request for a numerical answer. We've started discussing scattering matrices in my High frequency engineering class, and I'm having some trouble understanding wave mechanics. This got no attention in the homework forum, so I'll just copy paste from there. In a 2x2...
  32. D

    Scattering Parameters: Basic questions

    Scattering parameter say, S11, can be defined as the ratio of the reflected wave from port 1 to the incident wave on port 1. If it is a 2-port network, we imply the condition that the load at port 2 is matched to the characteristic impedance of the line. Take this excerpt from another...
  33. K

    Parametric equation of a surface-eliminating the parameters

    Homework Statement The parametric equation of a surface is given by: x = s + t, y = (s2/2) + s f(t) + t, u = s + f(t) where f is some given function (e.g. f(t)=t/2). I would like to eliminate s and t from these equations and describe the surface in terms of x, y and u only. Homework...
  34. S

    Singular point affected by parameters of ODEs

    Homework Statement I'm trying to solve a set of boundary value ODEs numerically, which contains about ten parameters. And i found that with some values of parameters, the solution may be singular at an endpoint(Maple says "system is singular at the righthand endpoint"). So i guess there...
  35. A

    Method of Variation of Parameters

    Allright, I understand that we need two solutions to be able to apply the method like y_{1} and y_{2} Problem gives 1 of them or let's you find only that 1 solution. But I can't apply the method since I don't have the other solution. The method I know is: u_{1}'(x)y_{1}(x)+u_{2}'(x)y_{2}=0...
  36. B

    Solving a first order linear differential equation by variation of parameters

    Homework Statement I have to solve the following differential equation by the "variation of parameters" method.Homework Equations \frac{dy}{dx}x +2y = 3x The Attempt at a Solution The associated homogeneous equation of the initial equation is: \frac{dy}{dx} = -2x^{-1}y So \frac{1}{y}dy =...
  37. Wellesley

    Variation of Parameters - Higher order DE

    Homework Statement Given that x, x2 and 1/x are solutions of the homogeneous equation corresponding to: x^3y''' + x^2y''-2xy'+2y=2x^4 x>0 determine a particular solution. Homework Equations The Attempt at a Solution I'm trying to solve this problem using three...
  38. R

    Free Parameters In String Theory

    Hello to all: I heard Michio Kaku talk on string theory recently and I thought I heard him say that the theory had no free parameters. But in thinking about the matter, I could not decide what that meant -- if it is true. Could someone please tell me what ingredients go into string theory...
  39. W

    Parameters, Arguments, Variables, Constants I`m confused,

    First of all, I understand what a constant is, what a variable is, and somewhat what a Parameter is. For parameters, as much as I know they are variables but of a specific type, for exmaple:- a^2= B, where B is the area of the square..now "a" is a variable, but its also a parameter, since...
  40. X

    Variation of parameters inhomogeneous DE help

    Ok here's my problem: 1. Solve the inhomogeneous second order de: x^2y" - 3xy' + 4y =x^4 2. Worked: y(p) = 1/4*x^4 Given: y(1) = x^2 y(2) = log(x)*x^2 3. I just need help getting the roots of the given de so i can determine y(h) of this de. As...
  41. D

    How can I use variation of parameters to solve this differential equation?

    Hey all, this is a little confusing, because the "variation of parameters" that I have been taught in class is different then what I find in most texts... I have y''' + y' = tan(x) Most textbooks use the wronskian and work from there, what I was taught to do is set it up as the...
  42. S

    Least Square Fit of Multiple Measurements with Shared Parameters

    Dear All, I would like to least square fit a number of measurements using several nonlinear functions with shared parameters (similar to the advanced fitting in Origin) using Mathematica. Therefor I would be interested in an Algorithm like Gauss-Newton that fits several data-set to several...
  43. A

    Graphing with Mathematica and Parameters

    Homework Statement Second part of Part C is: Use mathematica to draw graphs for a few values of the parameters. [ Consider the cases b > 0 and b< 0] Homework Equations I think you use the answer to Part A The Attempt at a Solution Not sure how to graph with mathematica...
  44. U

    Diff Eq: Variation of Parameters for 3rd-ODE's

    Homework Statement http://img27.imageshack.us/img27/6083/variationofparametersfop.jpg
  45. Y

    How do you relay EM wave parameters to Transmission line parameters?

    I am studying EM wave and transmission lines. I see both derive equations for propagation constant \gamma: Plane wave velocity is 1/\sqrt{\mu\epsilon} and \eta = \sqrt{\mu/\epsilon} Transmission line velocity is 1/\sqrt{LC} and Z0=\sqrt{L/C}. From that the book just to say the velocity...
  46. T

    Second Order ODE - Variation of Parameters

    Homework Statement Find the general solution of the following diff. eqn. y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0 Homework Equations General soln - Φgeneral(t) + Φparticular(t) Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t) The Attempt at a Solution I'm solving by...
  47. djeitnstine

    Variation of parameters method

    Homework Statement y''+y=tan(x)+e^{3x}-1 Homework Equations homogeneous solution: y_{hom..}=C_{1}cos(x)+C_{2}sin(x) particular solution: y_{parti..}=v_{1}' cos(x)+v_{2}' sin(x) The Attempt at a Solution v_{1}' cos(x)+v_{2}' sin(x)=0 (1) -v_{1}' sin(x)+v_{2}' cos(x) =...
  48. B

    Pelton wheel design parameters

    Would like to replicate a project we did in school for Turbomachinery class, which was to build a functioning hydropower turbine model. We were given the varous ideal parameters like bucket width, width to length ratio,number buckets and nozzle diameter based on size of wheel. Anyone know of any...
  49. J

    Solving the 1D Heat Equation with Given Parameters

    Problem:IF there is heat radiation within the rod of length L , then the 1 dimensional heat equation might take the form u_t = ku_xx + F(x,t) Find u(x) if F = x , k = 1 , , u(0)=0 , u(L) = 0 the problem is that i am not sure what this is asking me , how can i find u(x) if i have...
  50. B

    Understanding Laser Annealing Simulation Parameters

    Dear all, I have some problems with a program called the simulation of laser interaction with materials. In this program, they asked for some parameters which I am unsure of but I believe it has something to do with space grid for simulating the thermal conduction. This is a 1D heat...
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