Function Definition and 1000 Threads

I followed a demonstration in one of my electromagnetism books, but it is not clear to me. My problem is at the starting point. The book begins by considering the office defined in the following way: $$Q=\int d^4xJ^\alpha(x)\partial_\alpha\theta(\eta_\beta x^\beta)$$ where...

hi guys I was trying to verify the integral representation of incomplete gamma function in terms of Bessel function, which is represented by $$\gamma(a,x) = x^{\frac{a}{2}}\;\int_{0}^{∞}e^{-t}t^{\frac{a}{2}-1}J_{a}(2\sqrt{xt})dt\;\;a>0$$ i was thinking about taking substitutions in order to...

I have no problem in following the literature on this, i find it pretty easy. My concern is on the derived function, i think the textbook is wrong, it ought to be, ##S^{'}(t)##=##\frac {4t} {\sqrt{1+4t^2}}=0## is this correct? if so then i guess i have to look for a different textbook to use...

Hi everyone! I have a 8th order transfer function, you can see it in the first image: % Transfer function num = [2.091,0,203.3,0,-2151,0,-1.072e05]; den = [1,0,-830.4,0,-1.036e05,0,-5.767e05,0,2.412e07]; tf = tf(num, den) I need to use a PID, so I'm trying to use a compensator, adding poles...

Let ##\quad z=h(x, y)## and ##x=f(t) ; y=g(t)## Let the change in the function z be given by ##\Delta z=h(x+\Delta x, y+\Delta y)-h(x,y)## We can also write the change as ##\begin{aligned} \Delta z=h &(x+\Delta x, y)-\\ & h(x, y)-h(x+\Delta x, y) \\ &+h(x+\Delta x, y+\Delta y)...

I started out by finding the w (omega) value for all of the three states but I'm not sure where to go from there.

Hi everybody We can't differentiate ##x^x## neither like a power function nor an exponential function. But ##x^x=e^{x\mbox{ln}x}##. So ##\dfrac{d}{dx}x^x=\dfrac{d}{dx}e^{x\mbox{ln}x}=x^x(\mbox{ln}x+1)## And here comes the doubt: prove the domain of ##x^x## is ##(0, +\infty)## Why is only...

##f(x)=x^3+3x−1##

$\tiny{6.5.95 Kamehameha HS}$ Express y as a function of x. $\quad C>0$ $3\ln{y}=\dfrac{1}{2}\ln{(2x+1)}-\dfrac{1}{3}\ln{(x+4)}+\ln{C}$ rewirte as $\ln{y^3}=\ln{(2x+1)^{(1/2)}}-\ln{(x+4)^{(1/3)}}+\ln{C}$ then e thru and isolate y i think looks like it will be ugly

##x## is a function ##f(\alpha)## of ##\alpha##: $$\displaystyle x\, = \,\ln \left( {{\rm e}^{ 0.6931471806\,{\alpha}^{-1}}}-{{\rm e}^{ 0.2876820724\,{\alpha}^{-1}}} \right)$$ and ##y## is a function ##g(\alpha)## of ##\alpha##: $$\displaystyle y\, = \,\ln \left( {{\rm e}^{...

Hi, I have the following function, which is computed by: (x+n)/(x+y+n+m), where x, y are real numbers n, m are natural numbers What techniques I can use to smooth the function preventing it to jump up or down at an early stage. I would appreciate your suggestion. Thanks

I want to know the frequency domain spectrum of an exponential which is modulated with a sine function that is changing with time. The time-domain form is, s(t) = e^{j \frac{4\pi}{\lambda} \mu \frac{\sin(\Omega t)}{\Omega}} Here, \mu , \Omega and \lambda are constants. A quick...

Let f be a 2 variables function. 1) ##f(x,y)=g(x)+h(y)\Rightarrow df=g'(x)dx+h'(y)dy\Rightarrow\int df=g(x)+k(y)+h(y)+l(x)=f(x,y),\textrm{ if } k=l=0## 2) ##f(x,y)=xy\Rightarrow df=ydx+xdy\Rightarrow\int df=2xy+k(y)+l(x)\neq f(x,y)## Why in the second case the function cannot be recovered ?

I am not that super expert of statistics, so feel free to shift my formulation of the problem into the right one.First, for a physicist, the basic formulation of the problem. Let us say that you have a gravitational field and you have a fully symmetric problem on a flat world without other...

Ron Larson stated: "The domain of a function can be described explicitly or it can be implied by the expression used to define the function. The implied domain is the set of all real numbers for which the expression is defined." 1. How is a function defined explicitly? 2. How is a function...

Here is the fuzzy definition of a function as presented by Ron Larson. Definition of Function A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) of the function f, and...

Hi, I am looking for changing the logit f(z) = 1/(1+exp(-z)), where z range is [-inf,+inf]. I want to adapt it as follows: if z > 0.5 then f > 0.5 z < 0.5 then f < 0.5 Thanks

So I've been programming the BDF methods and for some reason I have an issue with the Backward Euler technique. Given the differential equation y" + y = 0 (with y(0) = 2, y'(0) = 0), my backward Euler solution goes like this: Obviously this is not possible as the function should be a...

Use the graph to investigate (a) lim of f(x) as x→2 from the left side. (b) lim of f(x) as x→2 from the right side. (c) lim of f(x) as x→2. Question 20 For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter...

My apologies. I posted the correct problem with the wrong set of instructions. It it a typo at my end. Here is the correct set of instructions for 28: Use the graph to investigate limit of f(x) as x→c. If the limit does not exist, explain why. For (a), the limit is 1. For (b), the limit DOES...

$\tiny{ACT.trig.01}$ What is the period of the function $f(x)=\csc{4x}$ $a. \pi \quad b, 2\pi \quad c. 4\pi \quad d. \dfrac{\pi}{4} \quad e. \dfrac{\pi}{2}$ well we should know the answer by observation but I had to graph it looks like $\dfrac{\pi}{2}$

Hello! So I need to find the potential function of this Vector field $$ \begin{matrix} 2xy -yz\\ x^2-xz\\ 2z-xy \end{matrix} $$ Now first I tried to check if rotation is not ,since that is mandatory for the potentialfunction to exist.For that I used the jacobi matrix,and it was not...

Let ##f,g:\mathbb{R}^2\longrightarrow\mathbb{R}## be defined, and denote ##D=f(\mathbb{R}^2)##. Assume without loss of generality that ##g(\mathbb{R}^2)\equiv f(\mathbb{R}^2)##. Define a function ##\varphi_f:D\longrightarrow \mathbb{R}^2## as follows: ##\varphi_f(z)=\{(x,y):f(x,y)=z\}##, and...

Summary:: Stoke stream function [Mentor Note -- Thread moved from the technical forums, so no Homework Template is shown] Why the quantity of fluid that crosses the surface of revolution formed by the vector OP is ?

If you are told something holds if the limit exists, and given a function f (specifically not piecewise defined), is it enough to show that the limit as x approaches c = the function evaluated at c? With a piecewise defined function, it is easy to check both sides of a potential discontinuity...

Problem statement : I start by putting the graph of (the integrand) ##f(x)## as was given in the problem. Given the function ##g(x) = \int f(x) dx##. Attempt : I argue for or against each statement by putting it down first in blue and my answer in red. ##g(x)## is always positive : The exact...

Problem: Let ## f: \Bbb R \to \Bbb R ## be continuous. It is known that ## \lim_{x \to \infty } f(x) = \lim_{x \to -\infty } f(x) = l \in R \cup \{ \pm \infty \} ##. Prove that ## f ## gets maximum or minimum on ## \Bbb R ##. Proof: First we'll regard the case ## l = \infty ## ( the case...

I'm trying to pass through some parameters of a function to the gsl integration routine but my code is currently not returning correct values. I attach a version of my code using dummy example functions and names. struct myStruct_t { double a; }; double func(double z, void* params)...

Hi, I am new here and hope I have posted my thread in the right forum. I have the following SIN function in Excel: =1*(SIN(2*PI()*1,6667*0,45)) The result is -1. That is what I want, so no problem. But what I want is a function that calculates the Time t value, in this example the value 0.45...

Hello! (Wave) I am looking at the following exercise: Find the solution $u(t,x)$ of the problem $$u_t-u_{xx}=2 \sin{x} \cos{x}+ 3\left( 1-\frac{x}{\pi}\right)t^2, t>0, x \in (0,\pi) \\ u(0,x)=3 \sin{x}, x \in (0,\pi) \\ u(t,0)=t^3, u(t, \pi)=0, t>0$$ At the suggested solution, it is stated...

Hey everybody, :smile: I have a joint density of the random variables ##X## and ##Y## given and want to find out ##P(X+Y>1/2)##. The joint density is as follows: $$f_{XY}(x,y) = \begin{cases}\frac{1}{y}, &0<x<y,0<y<1 \\ 0, &else \end{cases}$$ To get a view of this I created a plot: As...

How would you go about finding maximum value for this function without Calculus? You can draw in it a CAS tool like Geogebra, NSpire or Maple. And use the maximise ability. But is possible to do it by hand? Pre-Calculus?

Hi When we find integrals of Bessel function we use recurrence relations. But this requires that we have the variable X raised to some power and multiplied with the function . But how about when we have Bessel function of first order and without multiplication? How should we integrate it ?

Hey guys! Sorry if this is a stupid question but I'm having some trouble to express this charge distribution as dirac delta functions. I know that the charge distribution of a circular disc in the ##x-y##-plane with radius ##a## and charge ##q## is given by $$\rho(r,\theta)=qC_a...

I need to find the FT of this function. Here is my attempt: $$H(f) = \int_{0}^{\infty} ke^{-2 \pi i f t}dt$$ We know that ##\delta(t) = \int_{-\infty}^{\infty} e^{2 \pi i f t} df##, the part with sin in this integration vanish, so that, and knowing that cos is a even function, we can write...

We can rewrite |x-3|<10 in the following way. -10<x-3<10 But can rewrite |x-3|+|x+1|+|x|<10 in the following way? -10<x-3+x+1+x<10. If we cannot, will anybody please explain why we cannot?

Hello everyone. I have a vector, stochasticData.mat, it contains a matrix of size 211302*50, being 211302 measurements of 50 realizations of a stochsatic process. I want to use the Karhunen-Loève expansion and the software Mathematica to calculate the uncorrelated random variables. For that, I...

Good day, I have a question regrading how to find the absolute minima maxima of a function , I understand that first we need to calculate the Hessian Matrix to find the relative minima /maxim but after we need to check the borders of the region ( a rectangle in our case) for example we put x=-2...

Problem statement : Let ##f\in C^\infty ([-1;1])## with ##f(1)=f(-1)=0## and ##\int_{-1}^1f(x)dx=1## Which curve has the lowest (maximal) absolute slope ? Attempt : Trying to minimize ##f′(x)−\lambda f″(x)## with Lagrange multipliers but to find f not x ? I got...

Hey! :giggle: We have the function $$f(x,y)=\begin{cases}x^2\sin\left (\frac{1}{x}\right )+y^2\sin\left (\frac{1}{y}\right ) & \text{ if } xy\neq 0 \\ x^2\sin\left (\frac{1}{x}\right ) & \text{ if } x\neq 0, y=0 \\ y^2\sin\left (\frac{1}{y}\right ) & \text{ if } x= 0, y\neq 0 \\ 0 & \text{ if...

At first, I inverted the function(##f^{-1}(x)=g(x)##) and calculated the volume through the integral: $$V=\pi\int_{0}^{4}[4-(2-g(x))^2]\ dx$$ but then I questioned myself if the same result could have been obtained without inverting the function. To find such a strategy, I proceeded as follows...

I'm trying to solve for this in a deuteron problem. But can't seem to get the right answer. The reduced mass of the deuteron is 469.4 MeV, the binding energy Eb is 2.226 MeV and R = 1.5fm. Using hbar = 6.5817x10^-16 eV.s I get Kappa = sqrt((2(469.4)*2.226)/(6.5817*10^-22)^2) = 6.94*10^16...

We have a function: ## f(x,y)=\sqrt{\frac{1−2x}{1−y^2}} = \frac{\sqrt{1−2x}}{\sqrt{1−y^2}}## for small x and y, we can use standard approximations: ## 1/\sqrt{1−x}=1+x/2+... ## and ##\sqrt{1−x}=1−x/2−... ## Ok. Now we can approximate the whole function f(x,y) First method: ##...

Hello all. I have a question about building the coherent transfer function and specifically how I would go about deriving the pupil function for this figure. I have not come across this in my class yet and am a bit stumped. Any help would be appreciated.

A newbie who knows basic math is helping a five year old do his kindergarten project. The boy has to integrate a function ##f(x,y)## over the boundary of the first quadrant denoted ##\partial \Omega## where ##\partial\Omega = \{ x=0, y\geq 0 \} ∪ \{ x\geq 0, y=0 \} ## How would I explain to...

equation i need to proof. the N in here, is the avarege number of particles, N0 is the total number of particles,V is total volume, v0 I am not quite sure what it is because it isn't mentioned in the homework, but I am assuming it is the volume of which space.

Hello, Periodic trigonometric functions, like sine and cosine, generally take an angle as input to produce an output. Functions do that: given an input they produce an output. Angles are numerically given by real numbers and can be expressed either in radians or degrees (just two different...

Hi MHB! I recently came across a problem and I was thinking most likely I was missing something very obvious because I couldn't make sense of what was being asked, and I so wish to know what exactly that I failed to relate. Question: Find the minimum of $6\sin x+8\cos x+5$. Hence, find the...

hi, there. I am doing some frequency analysis. Suppose I have a function defined in frequency space $$N(k)=\frac {-1} {|k|} e^{-c|k|}$$ where ##c## is some very large positive number, and another function in frequency space ##P(k)##. Now I need integrate them as $$ \int \frac {dk}{2 \pi} N(k)...

Hi everyone, Imagine I have a system of linear differential equations, e.g. the Maxwell equations. Imagine my input variables are the conductivity $\sigma$. Is it correct from the mathematical point of view to say that the electric field solution, $E$, is a function of sigma in general...