Reputation
1,501
Top tag
Next privilege 2,000 Rep.
 Aug 2 suggested approved edit on Solving for $v$ in $v'(t) + R(t)\cdot v^{2/3}=J(t)$ Aug 2 comment What does “$f$ is a function on $S$” mean? I am guessing the exact expression of $f$ will provide image. Aug 2 comment What does “$f$ is a function on $S$” mean? $S$ is a domain. The codomain is any superset of the image of $S$ under $f$. Aug 2 comment Is this a function? Thanks for that. :-) +1 Aug 2 comment Is this a function? @HenningMakholm: Okay, thanks. I was not aware of this notation. So you are saying the notation is equivalent to the below? $$\theta(x,y) = (3y,2x,x+y)$$ Aug 2 comment Is this a function? @Mathh Pressland: I do not believe the co-domain is $\mathbb{R}^{3}$, rather I believe the co-domain is a vector space $W$ where an element of $W$ is $w$ of the form $(u,v)$ where $u \in \mathbb{R}^{2}$ and $v \in \mathbb{R}^{3}$. This space might be isomorphic to $\mathbb{R}^{3}$ though. Aug 2 comment Is this a function? Yes, it is a function. Domain is $\mathbb{R^{2}}$ and co-domain is $V\times W$ where $V$ is a vector space over $R$ of dimension $2$ and $W$ is a vector space over $R$ of dimension 3. Aug 2 comment hints on solving DE Yeah, can happen. ;-) Aug 2 comment hints on solving DE Sorry for the $\frac{a}{2}$, it should be only a Aug 2 answered hints on solving DE Aug 2 comment hints on solving DE You must have made different substitutions. I am getting the following. $$\frac{dw}{dz} = \frac{w-\frac{a}{2}z}{z-aw}$$ I will write a partial answer for you. Aug 2 comment hints on solving DE No, basically you then eliminate $x$ and $y$ and solve for $w$ in terms of $z$. If you want more hint, I can give you so. Aug 2 comment hints on solving DE Try putting $w^{2} = x^{2} + y^{2} + z^{2}$ and then use the identity $$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{k_{1} a + k_{2} c + k_{3} e}{ k_{1} b+ k_{2} d+ k_{3} f}.$$ Aug 1 awarded Yearling Jul 31 comment Limit of binomial coefficient @J.M., Thanks for the info. Jul 31 comment Limit of binomial coefficient @J.M. : He is using the notation for combination, so probably he means a non-negative integer? Jul 30 comment Approximated Laplace transform of a non-linear system Jul 30 comment Approximated Laplace transform of a non-linear system $\dot{\omega}(t) \approx \alpha_0 \omega(t) + \beta_0 i(t)$ is a valid assumption for only $t \approx 0$ since $\dot{\omega}(t)$ is largely negative and very large and stays like that until $\omega\left(t\right)$ is very small. So, that is one source of error. Jul 30 comment Approximated Laplace transform of a non-linear system If you can give me approximate regions (in terms of actual values of $\omega$ and $i$ in which you want the solution, it might be better/easier to solve. I can solve it most probably even if you are able to provide the value of $\omega(t)$ as $t \rightarrow \infty$. Jul 29 comment Open mapping of the unit ball into itself Ohh, right. Sorry. I missed the open part. So careless of me.