Solution to set of harmonic equations The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Calculating maximum of functionAbsolute maximum and minimum value of continuous function on interval $I = [a, b]$Is there a better way to find the minimum value of $displaystylefrac1sin theta cos theta left ( sin theta + cos theta right )$Find the maximum and minimum values of $sin^2theta+sin^2phi$ when $theta+phi=alpha$Harmonic Function - Multivariable calculusOptimization with LagrangeStrong Maximum Principle proof (for harmonic functions in the plane)What's the intuition of the general rule of finding maxima and minima?How do I find the maximum and minimum $y$ values of this function?Find the highest and lowest possible value of function $f(x)=3x^2+6x+6over x^2+4x+5$
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Solution to set of harmonic equations
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Calculating maximum of functionAbsolute maximum and minimum value of continuous function on interval $I = [a, b]$Is there a better way to find the minimum value of $displaystylefrac1sin theta cos theta left ( sin theta + cos theta right )$Find the maximum and minimum values of $sin^2theta+sin^2phi$ when $theta+phi=alpha$Harmonic Function - Multivariable calculusOptimization with LagrangeStrong Maximum Principle proof (for harmonic functions in the plane)What's the intuition of the general rule of finding maxima and minima?How do I find the maximum and minimum $y$ values of this function?Find the highest and lowest possible value of function $f(x)=3x^2+6x+6over x^2+4x+5$
$begingroup$
I have a function
beginequationlabelequ:Ac_theta
f(theta) = A_7sin(7cdot theta)+...+A_17sin(17cdot theta)
endequation
I am interested in finding the value of second highest maximum or minimum of $mid f(theta) mid$. Given a set of amplitudes, for example $[A_7...A_17]=[7...17]$ I can find the value of theta where $mid f(theta) mid$ attains the second highest local maximum/minimum. My questions are as follows
1.If I change the value of one of the amplitude or multiple amplitudes then is it possible to find out the value $mid f(theta) mid$ given the fact that the value of $mid f(theta) mid$ is known for at least one set of amplitudes? So does a relation exist that $theta = f([A_7...A_17])?$
- if $[A_7...A_17]neq[7...17]$ then is it at least possible to guess whether the value of $mid f(theta) mid$ will be higher or lower than when $[A_7...A_17]=[7...17]$?
My conclusion so far is there is no way of telling which direction the value of $mid f(theta) mid$ will go by changing the co-efficient. In other words according to me no such relation exist. I will have to find the value of $mid f(theta) mid$ numerically using Matlab or such and if my goal is to find a value of $mid f(theta) mid$ which is lesser than the given set of co-efficient then I will simply have to try all combinations of co-efficient till I find such a value. This means a lot of computational effort.
calculus functions harmonic-functions
asked Mar 31 at 14:41
RANRAN
134
$endgroup$
add a comment |
$begingroup$
I have a function
beginequationlabelequ:Ac_theta
f(theta) = A_7sin(7cdot theta)+...+A_17sin(17cdot theta)
endequation
I am interested in finding the value of second highest maximum or minimum of $mid f(theta) mid$. Given a set of amplitudes, for example $[A_7...A_17]=[7...17]$ I can find the value of theta where $mid f(theta) mid$ attains the second highest local maximum/minimum. My questions are as follows
1.If I change the value of one of the amplitude or multiple amplitudes then is it possible to find out the value $mid f(theta) mid$ given the fact that the value of $mid f(theta) mid$ is known for at least one set of amplitudes? So does a relation exist that $theta = f([A_7...A_17])?$
- if $[A_7...A_17]neq[7...17]$ then is it at least possible to guess whether the value of $mid f(theta) mid$ will be higher or lower than when $[A_7...A_17]=[7...17]$?
My conclusion so far is there is no way of telling which direction the value of $mid f(theta) mid$ will go by changing the co-efficient. In other words according to me no such relation exist. I will have to find the value of $mid f(theta) mid$ numerically using Matlab or such and if my goal is to find a value of $mid f(theta) mid$ which is lesser than the given set of co-efficient then I will simply have to try all combinations of co-efficient till I find such a value. This means a lot of computational effort.
calculus functions harmonic-functions
asked Mar 31 at 14:41
RANRAN
134
$endgroup$
add a comment |
$begingroup$
I have a function
beginequationlabelequ:Ac_theta
f(theta) = A_7sin(7cdot theta)+...+A_17sin(17cdot theta)
endequation
I am interested in finding the value of second highest maximum or minimum of $mid f(theta) mid$. Given a set of amplitudes, for example $[A_7...A_17]=[7...17]$ I can find the value of theta where $mid f(theta) mid$ attains the second highest local maximum/minimum. My questions are as follows
1.If I change the value of one of the amplitude or multiple amplitudes then is it possible to find out the value $mid f(theta) mid$ given the fact that the value of $mid f(theta) mid$ is known for at least one set of amplitudes? So does a relation exist that $theta = f([A_7...A_17])?$
- if $[A_7...A_17]neq[7...17]$ then is it at least possible to guess whether the value of $mid f(theta) mid$ will be higher or lower than when $[A_7...A_17]=[7...17]$?
My conclusion so far is there is no way of telling which direction the value of $mid f(theta) mid$ will go by changing the co-efficient. In other words according to me no such relation exist. I will have to find the value of $mid f(theta) mid$ numerically using Matlab or such and if my goal is to find a value of $mid f(theta) mid$ which is lesser than the given set of co-efficient then I will simply have to try all combinations of co-efficient till I find such a value. This means a lot of computational effort.
calculus functions harmonic-functions
asked Mar 31 at 14:41
RANRAN
134
$endgroup$
I have a function
beginequationlabelequ:Ac_theta
f(theta) = A_7sin(7cdot theta)+...+A_17sin(17cdot theta)
endequation
I am interested in finding the value of second highest maximum or minimum of $mid f(theta) mid$. Given a set of amplitudes, for example $[A_7...A_17]=[7...17]$ I can find the value of theta where $mid f(theta) mid$ attains the second highest local maximum/minimum. My questions are as follows
1.If I change the value of one of the amplitude or multiple amplitudes then is it possible to find out the value $mid f(theta) mid$ given the fact that the value of $mid f(theta) mid$ is known for at least one set of amplitudes? So does a relation exist that $theta = f([A_7...A_17])?$
- if $[A_7...A_17]neq[7...17]$ then is it at least possible to guess whether the value of $mid f(theta) mid$ will be higher or lower than when $[A_7...A_17]=[7...17]$?
My conclusion so far is there is no way of telling which direction the value of $mid f(theta) mid$ will go by changing the co-efficient. In other words according to me no such relation exist. I will have to find the value of $mid f(theta) mid$ numerically using Matlab or such and if my goal is to find a value of $mid f(theta) mid$ which is lesser than the given set of co-efficient then I will simply have to try all combinations of co-efficient till I find such a value. This means a lot of computational effort.
calculus functions harmonic-functions
calculus functions harmonic-functions
asked Mar 31 at 14:41
RANRAN
134
asked Mar 31 at 14:41
RANRAN
134
edited Mar 31 at 14:53
RAN
asked Mar 31 at 14:41
RANRAN
134
asked Mar 31 at 14:41
RANRAN
134
asked Mar 31 at 14:41
RANRAN
134
134
add a comment |
add a comment |
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