Peter Kowalski
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 Sep 4 comment Calculate the flux through a surface S and my approach using Divergence theorem Thank you. I modified my solution, you can quickly skim through and check if now it is correct. One question though - this equation $$\frac{\partial}{\partial x}(r^2x) = \frac{\partial (r^2)}{\partial x}x + r^2$$ consists of two parts summed together, because it is the derivative of a multiplication. Am I right? Sep 4 comment Calculate the flux through a surface S and my approach using Divergence theorem Apparently no. Can you describe in detail how did you get from $\vec{F} = (r^2x, r^2y, r^2z)$ to $5r^2$. For me it looks like te result should be $6r^2$, since the derivative of $r^2x, r^2y, r^2z$ versus $dx, dy, dz$ respectively is $3 \cdot r^2=6r^2$. Am I right? Sep 4 comment Calculate the flux through a surface S and my approach using Divergence theorem Can you please show me what should I put under $div$ operator. I am trying and still do not know how to proceed. I can't figure out how did you get that $div \vec{F}$ is $5r^2$ Sep 4 comment Calculate the flux through a surface S and my approach using Divergence theorem So, should the $\vec{F}$ be equal to $(x^3+y^2x+z^2x)+(x^2y+y^3+z^2y)+(x^2z+y^2z+z^3)$? Sep 4 comment Calculate the flux through a surface S from a field described by vectors I have created a new topic as you advised. math.stackexchange.com/questions/1421867/… Sep 4 comment Calculate the flux through a surface S and my approach using Divergence theorem @JakeLebovic How should it look like then? Sep 4 comment Calculate the flux through a surface S from a field described by vectors @michaelrccurtis Thank you for answering. I just want to clarify if "2. No" means "No, this normal vector is not supposed to be used here". And regarding the 1. - I still can't figure out how did you get that $div\vec{F}$ is $5r^{2}$ from $(x^2 + y^2 + z^2) (x,y,z)$ which for me is equal to $x^3+y^3+z^3$? Sep 3 comment Calculate the flux through a surface S from a field described by vectors Please check my EDIT, I have added a solution and I don't know if it is correct. Sep 3 comment Calculate the flux through a surface S from a field described by vectors Thank you. Why does it take the form of $(x^2+y^2+z^2)$ and not $(x^2,y^2,z^2)$ - I mean why do you add the vector components together? Ad. 3 I would have calculated it, but I wanted to make sure the $\vec{F}$ is correct. Sep 3 comment Calculate the flux through a surface S from a field described by vectors Yes, you are right with the first, that it should be $\vec{F} \cdot \vec{ds}$. But regarding the second point - it should have a symbol of $\unicode{x222F}$ but I couldn't make it work. Sep 2 comment Divergence theorem and applying cylindrical coordinates At first I substituted $x^2+y^2=1$. Thank you for your suggestion, but still the obtained answer is presumably incorrect. Please check my Edit. Sep 2 comment Divergence theorem As advised, I created a post with my question here - math.stackexchange.com/questions/1418983/… Aug 31 comment Divergence theorem Hello. I have trouble with your answer - can I change the $dxdydz$ to another coordinates? What would be the cylindrical coordinates and their range in this case? Aug 31 comment Calculate the flux through a closed surface @JakeLebovic Thank you. So apparently after calculating $P_{x}, Q_{y}, R_{z}$ the exercise is finished? Aug 26 comment Line integral and checking its path independence in three dimensions Thank you for the edited answer. 1) Did you get $U(1,0,0)$ by substituting $12 \pi$ (and then 0) into $\gamma(t)=(\cos^{4}t,\cos t\sin^5t,\sin^4t)$? 2) Could the task be finished after this substitution, since the $\gamma$ is a closed curve? 3) What if the $\gamma$ is not a closed curve? Aug 25 comment Line integral and checking its path independence in three dimensions Thank you for the answer. I have two questions regarding it: 1) Why did you write that $g$ is a constant and not $0$? 2) Why did you substitute $(1,0,0)$ under $U$? 3) Then why do I need the info about $\gamma(t)=(\cos^{4}t,\cos t\sin^5t,\sin^4t)$ and $t \in[0,12\pi]$ in the exercise? Aug 25 comment Line integral and checking its path independence in three dimensions Yes $P′x$ is the partial derivative of $P$ with respect to $x$. How did I get to $U=xycos(yz)$? You are right, I confused $U_{y}$ with $U$. How should I continue? Aug 22 comment Finding the mass of a curve having a specified linear density using a line integral Thank you very much. Now I understand why wolfram was giving me 0. Apparently my computation was right despite the mistake with the absolute value. Dec 18 comment Finding volume of a shape using double integral Thank You, what program do You use for that?