For example, in linear differential equations, there might be these questions where we'd directly use e∫pdx as the integrating factor and then substitute it in this really cliche formula but I never really understood where it came from. Help ?
I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this?
P(r) = ∫p(r) dr = exp(-μr)
p(r) = dP(r)/(4πr²dr)
One way I tried to...
1. The problem statement, all variables, and given/known data
Task begins by giving sample function and a corresponding Fourier transform $$f(t) = e^{-t^2 / 2} \quad \Longleftrightarrow \quad F(\omega) = \sqrt{2 \pi} e^{-\omega^2 / 2}$$ and then asks to find the Fourier transform of $$f_a(t) =...
Homework Statement
Determine the Fourier-transfroms of the functions
\begin{equation*}
a) f : f(t) = H(t+3) - H(t-3) \text{ and } g : g(t) = \cos(5t) f(t)
\end{equation*}
and
\begin{equation*}
b) f : f(t) = e^{-2|t|} \text{ and } g : g(t) = \cos(3t) f(t)
\end{equation*}
Homework Equations...
Hey guys,
I need your help. I am not sure if this is the right part of the forum to ask this question.
So I started reading papers about the Lyapunov Exponent, but there is something I do not understand in the formula. Why ? It seems logical that we want because we want to get the Exponent...
Homework Statement
Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not?
Homework Equations
8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)
The Attempt at a Solution
Brought all e^(ax) values to one...
How do I write taylor expansion of a function of x,y,z (not at origin) as an exponential function?
Please see the attached image. I need help with the cross terms. I don't know how to include them in the exponential function?
Homework Statement
In writing the definition of ##e## i.e. ##e=\displaystyle\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n##, why do we denote the variable by 'n' despite the fact that the formula holds for n∈(-∞,∞)? Is there any specific reason behind this notation i.e. does the variable have...
Homework Statement
superman has been disabled by a nearby amount of kryptonite, which decays exponentially. If Superman cannot regain his power until 90% og the kryptonite disintegrates, then how long will it be before he regain his powers?
Use r=-0.138629. Round to the nearest day.
a. 4days...
Homework Statement
[/B]
I need to differentiate the exponential function i = 12.5 (1-e^-t/CR) and I need to plot a table so that I can do a graph of i against t but i'm not sure how. (CR is the equivelant of Capacitance 20 Micro Fards and Resistance 300 Kilo Ohms)
Homework Equations
[/B]
How...
Homework Statement
The graph goes through the points (-2, 13) and (0, 5) and has the horizontal asymptote y = 4.
f(−2) = ____ therefore:
____(B^____ ) = ____
b =
The Attempt at a Solution
f(−2) = 13 therefore:
1 (B^-2 ) = 13
b = ? not sure
Thank you