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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What's the differences between multi variable and vector calculus

This is a conceptual question. If we use vector calculus and multi variable calculus as synonym, will it be completely wrong? If so what topics does multi variable calculus have but vector ...
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Why is divergence defined as $\mathbf{\nabla} \cdot \mathbf{v}$?

Suppose I am working in $\Bbb R^3$. Suppose I have a pond and I drop some dust on the surface. If the materials spread out, I have positive divergence, usually. Let $\mathbf{v}(\mathbf{x})$ denote ...
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What are the limits for this triple integral?

This is probably a very easy/silly question, but still I'm not sure about it. I want to calculate the volume of a body bound between the graph of $x^2+y^2-z^4=1$ (what does it look like?) and the ...
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Derivative of position [duplicate]

[Beginning calculus question.] I saw in a calculus lecture online that for a position vector $\boldsymbol{r}$ $$\left|\frac{d\boldsymbol r}{dt}\right| \neq \frac{d\left| \boldsymbol r \right|}{dt}$$ ...
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Minimal c satisfying $x+y-(xy)^c \geq 0$ for all $x,y\in [0,1]$

What is the minimal real $c$ satisfying $x+y-(xy)^c \geq 0$ for all $x,y \in [0,1]$? Experimentally (though my experiments weren't necessarily accurate enough) I reached as low as $c=\tfrac{13}{32}$, ...
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Einstein Summation with Del Operator

Can someone show explicitly me why $2B_k\nabla B_k = \nabla B^2$ ? Is $B_k\nabla B_k$ just $B_x\nabla B_x+B_y\nabla B_y+B_z\nabla B_z$? But then I end up with nine terms on the LHS and I can't ...
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