What is Variables: Definition and 1000 Discussions
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.
In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.
A bound variable is a variable that was previously free, but has been bound to a specific value or set of values called domain of discourse or universe. For example, the variable x becomes a bound variable when we write:
For all x, (x + 1)2 = x2 + 2x + 1.
or
There exists x such that x2 = 2.
In either of these propositions, it does not matter logically whether x or some other letter is used. However, it could be confusing to use the same letter again elsewhere in some compound proposition. That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.
The term "dummy variable" is also sometimes used for a bound variable (more often in general mathematics than in computer science), but that use can create an ambiguity with the definition of dummy variables in regression analysis.
Hello,
I am going through Whittaker's treatise on Classical Mechanics. In chapter 3 he derives the equation of motion for a simple pendulum, and I have a question about his method.
Starting from the general form for the equation of energy (s is the path):
\frac{m}{2}\dot{s}^2 =...
Hey guys and gals, this isn't actually an assignment of any sort, so I didn't want to put it in the homework section. This is also my first post, though I have been lurking for quite a while, reading the copious amounts of information available here. :p
Anyhow, could somebody please elaborate...
Homework Statement
In double integrals, the change of variables is fairly easy to understand. With u = constant and v = constant, along line KL v = constant so dv = 0. Therefore the only contributing variable to ∂x and ∂y is ∂v.
The Attempt at a Solution
However, in tripple...
I have a differential expression that I want to expand to some order around infinity (it's for calculating weak-field limits in GR). I have two functions, B(r) and n(r), and some expression involving them along the lines of
n[r] (3 r B'[r]^2 - 4 B[r] (2 B'[r] + r B''[r]))
Basically I want...
$x^2+m^2=2mx + (nx)^2$, $n\neq1$, $n\neq-1$
isolate $x$
rewriting
$m^2-2 m x-n^2 x^2+x^2 = 0$
$m(m-2x)-x^2(n-1)(n+1)=0$
I set this to 0 thinking I could factor by grouping but not..
So seem to be stuck on how to to isolate x
the books answere to this is $\frac{m}{1-n},\frac{m}{1+n}$
thnx...
Homework Statement
The probability of being dealt a full house is approximately 0.0014. Find the probability that in 1000 hands of poker you will be dealt at least 2 full houses
Homework Equations
I can use binomial distribution.
The Attempt at a Solution
The probability of getting...
Hi everyone,
I'm a Physics student going into my Junior year and I'm currently registering for my courses for the following semester and I have two options for my "complex" course, namely:
---------------------------------------------------
Complex Variables
Theory of functions of one complex...
Homework Statement
ac + bc = (a - c)(a + b) - xabcd^2
Homework Equations
Various factoring rules (difference of two squares, etc.)The Attempt at a Solution
I got it expanded to:
ac + bc = a^2 + ab - ac - bc - xabcd^2\\0 = a^2 + ab - 2ac - bc - bd - xabcd^2
I tried factoring different ways...
I am struggling with this question which appears in every adv. calculus exam paper I practise and would love some help or advice on how to even approach it! I have no trouble getting the extreme points and determining whether they are local minimum, local maximum or saddle points, but proving...
Homework Statement
I am performing a change of variables, s --> t and am wondering can I just write g(s) --> g(t) or do I have to alter the function e.g. g(s) --> a*g(t).
Homework Equations
s = (a/b)* t
g(s) is to be found numerically and therefore we do not have it's definition.
So...
Hi. I borrowed many multivariable Calculus book so that I can choose one for the next semester. The one I liked most is Multivariable Calculus by Ron Larson. It is full of graphics and colours, somthing that is essential to understand functions of two variables. The only thing is that it does...
i have a question.
i just try to learn MATLAB however i couldn't define the functions and variables inside the one script. i open new script file and give the function comment in it for example like this...
function [ y ] = betaf( x,Ee)
lambda=0.1;
y=100*gammaf(Ee)*lambda/(2*pi*x)...
Hi All,
I've managed to confuse myself with a simple change of variables.
I have an integral of the form:
$$
I = \int_f^{\infty} dt \int_0^1 ds\, t\, F(t(1-s),ts),
$$
where $F(a,b)$ is some well behaved function and $f$ is a positive number. I want to change variables:
$$
x =...
Mathematica:Solving two equations with two variables ??
Hi,
I am trying to solve two equations with two unkonwn variables. These equations are equal to zero so my way was first picking one of the variable to one side of the equations and equalize them and find the other unknown parameter...
How to solve this system?
\begin{align}
& \sqrt{\frac{x_{1}^{2}x_{4}^{2}}{4}-{{({{x}_{1}}-{{x}_{4}})}^{2}}}-\sqrt{\frac{x_{1}^{2}x_{3}^{2}}{4}-{{({{x}_{1}}-{{x}_{3}})}^{2}}}=\sqrt{\frac{x_{3}^{2}x_{4}^{2}}{4}-{{({{x}_{3}}-{{x}_{4}})}^{2}}} \\
&...
∫∫9(x + y) e^(x2 − y2) dA, where R is the rectangle enclosed by the lines x−y=0, x−y=10, x+y=0, and x+y=5
Relevant Equations:
The Jacobian: ∂(x,y)/∂(u,v)
The attempt at a solution:
I began by making u=x+y and v=x^2-y^2
So, u=0 and u=5, but I don't know what to do with the x-y line...
1. A scientist is investigating the effect of different types of radiation on the surface of a piece of Sodium metal. He uses a freshly cut surface on a Sodium plate.
2. a) Which of the variables is the dependent and independent variables?
b) Why must the surface of the Sodium...
"separation of variables", but for 2nd order
Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0
so turn this into u''/u'=-2cosx/sinx
At this point I...
Hi all.
This is my problem. I have two IDL procedures
hr2altaz, hour, dec, alt, az -- which takes the HA and DEC and
converts it to ALT and AZ
altaz2hr, hour, dec, alt, az -- which takes ALT and AZ, and converts
it to HA and DEC.
What I need to do, is to begin with a certain HA and DEC...
Consider the differential equation
where I''+I=e^it where i= sqrt (-1)
So I don't know what to do. I do know that The second derivative of
c*t*e^(i*t) is
-c e^(i t) (-2 i+t)
But I don't know what to do for a and b and I need help to get threw this problem before I take my test...
hi,
i want to take an x-y data set and find the deviation from another dataset.
the master dataset is two identical y=1/x curves of different amplitude; also one only registers at periodic intervals and the second is multiplied by a noise signal.
so part of the problem is going to be...
Homework Statement
Let's say the independent variable (in statistical terms) A depends on variables B, C and D. We perform tests, and find out that the variable A causes "something" with the values of B, C and D equal to B2, C2 and D2.
Let's also say that A with variables B, C and D of B1...
Hi,
In Griffiths QM, it is claimed that to solve the Schrodinger Equation, we take the solution wavefunction \Psi(x,t) to be of a seperable form \psi(x)\phi(t).
He then says that a superposition of these seperable forms can always give us the general solution. Can someone help me prove that...
I was reading over a textbook that stated the following, where y(s,t) = v(x(s,t),t)
\frac{\partial y}{\partial t} = \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial v}{\partial t}
and
\frac{\partial^2y}{\partial t^2} = \frac{\partial^2 v}{\partial x^2}\left (...
Hi all! I'm sorry if this question has been already asked in another post...
I'm studying the path integrals formalism in QED. I'm dealing with the functional generator for fermionic fields. My question is:
The generating functional is:
$$Z_0=e^{-i\int{d^4xd^4y \bar{J}(x)S(x-y)J(y)}}$$...
For single variable functions derivative means slope of tangent what does it mean for functions of more than one variable.
book says that a function is said to be differentiable if:
f(x + Δx , y + Δy) - f(x , y) = AΔx + BΔy + ε'ψ(Δx , Δy) + εh(Δx , Δy)
WHERE ε, ε' → 0 AS Δx , Δy → 0...
Homework Statement
f(1/u,0)=1 and f(0,1/u)=-1 for all positive (integer) values of u. Prove whether or not the limit as (x,y) ->(0,0) exists.
Homework Equations
none.
The Attempt at a Solution
I argue that 0,0 is not in the domain of the function, but this neglects the behavior of f(x,y)...
Homework Statement
I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y.Homework Equations
The Attempt at a Solution
X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with...
Hi,
The change of variables theorem states that given a diffeomorphism g:A \rightarrow B between open sets, and a continuous function f:A \rightarrow R, then
\int _A f = \int _B f \circ g |Det Dg| given that either one of the integrals exist.
I was wondering if anyone here could help explain...
I have an assignment where we have to ask the user for a number of data points which then we will graph a linear regression.
Enter the number of input data points: 7
Enter [x y] pair for point 1: [1.1 1.01]
Enter [x y] pair for point 2: [2.2 2.30]
Enter [x y] pair for point 3: [3.3 3.05]...
Hi,
I have some experimental data from a colleague which has been collected with different values for 7 parameters. It isn't nice, as in it's not as if 6 of the parameters were held fixed while the seventh was adjusted. Beyond that, I don't have much data. I'm not up on my statistical...
Not really a specific problem, but just a general question:
Does anyone have any good references (preferably online) for solving E&M problems with this method? I'm using Griffith's Electrodynamics book for my class and I'm trying to get ready for a final. This is the only part I'm having...
Homework Statement
Locate and classify the critical points of f(x,y) = (x-y)(xy-1).
Homework Equations
The Attempt at a Solution
I found the partial derivatives with respect to x and y and I got:
∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1
After setting them both equal to zero I can't...
I have read in different places something like the following:
Hermitian operators have real eigenvalues
Hermitian operators/their eigenvalues are the observables in Quantum Mechanics e.g energy
I am not sure what this means physically.
Let us say I have a Hermitian operator operating on a...
I have such MATLAB problem: I create variables R1 RF R2 and w so:
Code:
syms RF R1 R2 w
then I write expression:
Code:
3*R1*w*(RF + 200)/((R2*w*29*i + 3)*(3*R1*w - 2*i))
which gives:
Code:
(3*R1*w*(RF + 200))/((3*R1*w - 2*sqrt(-1))*(R2*w*29*sqrt(-1) + 3))
why sqrt(-1) and not i...
Hi!
I have a problem with the following equation:
log(D)-b*log(K) = b*log(z)-log(c)
I would like to get D and K on one side of the equal to sign, so that:
f(D,K) = g(b, c, z)
Is this possible?
Peter
Hi,
I'm new to MATLAB and programming, but I hoping to find out if I can have a variables in my program take on certain values only for certain time intervals. For example, I am using ode23s to solve some equations for me, but for the time interval [0,10] I would like one of the variables...
Homework Statement
solve dy/dx=e^(3x+2y) by separation of variables
The Attempt at a Solution
\frac{dy}{dx}=e^{3x+2y}
\frac{dy}{dx}=e^{3x}e^{2y}
e^{-2y}dy=e^{3x}dx
\int e^{-2y}dy=\int e^{3x}dx
e^{-2y}=-\frac{2}{3}e^3x + C
-2y = ln(-\frac{2}{3}e^{3x}+C)...
Homework Statement
The Fortran 90 code shown below was written to solve a Crank-Nicholson algorithm that describes the motion of a quantum particle (hence the need for complex numbers). Probably not that crucial to know the details of the math/physics, just the code...
The problem is that...
Hi, guys,
Why do we assume Lagrangian Density only depend on field variables and their first derivative?
Currently, I am reading Ashok Das's Lectures on Quantum Field Theory.
He says (when he is talking about Klein-Gordon Field Theory):
"In general, of course, a Lagrangian density...
I have seen the following "extension" of discrete random variables definition, from:
pediaview.com/openpedia/Probability_distributions
(Abstract)
"... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...
Hi all
I am trying to do a MATLAB plot, just like the one attached.
DATA: Graph shows a parameter (suppose) humidity along the height from ground upto 6 Km. Instrument measures humidity at each 30 meter height from the ground. Sample is repeated after each 15 minutes.
DATA FORMAT: Data...
Homework Statement
Let x=ts^2 -1 and y=ln(s)-t
Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1)
The Attempt at a Solution
y=ln(s)-t
∂f/∂t= ∂f/∂s X ∂s/∂t -1
t=x+1/s^2
∂t/∂s= -2(x+1)/s^3
∂s/∂t=s^3/-2(x+1)
∴ ∂f/∂t= s^2/-2(x+1)...
I have an equation that I am trying to change the variables of, it has the form;
\frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z
Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written...
i just came to learn that the intensive gas variables like pressure and temperature don't depend on the system size. now suppose , i sliced out a gas container into an imaginary plane and i got the extensive variable of volume and internal kinetic energy to be halved..
but why shouldn't the...