# Tagged Questions

Use this tag for questions about differential and integral calculus with more than one independent variable. Some related tags are (differential-geometry), (real-analysis), and (differential-equations).

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### calculate area using stokes

Let $S:= \{(x,y,z) | z = -x-y \} \cap \{(x,y,z) | z^2+y^2+x^2 \leq 1\}$ I have to calculate the Area of $S$. Since $S$ is the unit circle. I know that the area is $\pi$ But I have to use Stokes. I ...
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### Is $(0,0)$ is a singular point of $f(x,y) = x$

I have a little confusion regarding the following statement from Wikipedia: The singular points are those points on the curve where both partial derivatives vanish I can see that for the ...
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### Is this notation common in Calculus?

Okay this is going to be quite a stupid question, but to me this seems... wrong, or at the very least not completely correct. In the material I'm reading there's a part that states that $y$ evolves ...
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### How can I find the measure of $B=\{(x,y,z) \in\mathbb R^3| \; x^2+y^2+4z^2 \le3, \;x^2-y^2+4z^2\le1, \; z\ge 0\}$? [on hold]

$B=\{(x,y,z) \in\mathbb R^3| \; x^2+y^2+4z^2 \le3, \;x^2-y^2+4z^2\le1, \; z\ge 0\}$ The question is similar to that which I shared in another topic. Also here, the set is defined by an ellipsoid, ...
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### How to find a suitable function for Dulac's criteria in this example?

I have a system of odes $\dot{\mathbf{x}} = \mathbf{f(x)}$ where $\mathbf{x} \in \mathbb{R}^{2}$ and $\mathbf{f(x)}$ is defined below: $$\dot{x} = x- y - x^{3}, \qquad \dot{y} = x+y-y^{3}$$ I would ...
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### Calculating the Stokes Theorem

I was tasked with calculating $\oint_{L}Fdr$ for when $F=xzi-j+yk$ (vetor form) and $$L = \begin{cases}z=5(x^2+y^2)-1 & \mbox{ } \mbox{} \\z=4 & \mbox{} \mbox{} \end{cases}$$ Using: ...
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### Eliminate the parameter

Given the parametric equations: $x = sin(\frac{1}{2} \theta)$ $y = cos(\frac{1}{2} \theta)$ Eliminate the parameter. I am completely lost. Please help.