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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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Question about definition
I have a very naive question about the definition of the operator $(1+x)\partial_x$ as an operator $C^1 (\mathbb{R})\to C^0(\mathbb{R})$. Is it $A u = (1+x)\partial_xu$ in the sense that we have $Au(-... real-analysis multivariable-calculus derivatives- 127
A linear change of variables in a PDE, basic help
Consider the PDE to be solved for $f$, and for a given vector field $b:\mathbb{R}^n\to\mathbb{R}^n$ $$ \partial_t f(t,x)=\text{div}(b(x) f(t,x)),~\forall~t,x \in \mathbb{R}_+\times \mathbb{R}^n, $$ ... real-analysis multivariable-calculus chain-rule change-of-variable jacobian- 1
table of parametric surfaces with differentials
Can you send me a free opensource document best would be a pdf, that lists all the common surfaces (sphere cilinder torus cone etc) of parameters and they normal vectors calculated at once. That would ... multivariable-calculus reference-request- 121
Calculate the total derivative
Calculate directly the total derivative (without using partial derivatives) of the function $f(x_1,x_2)=x_1^2-10x_2$. You may wish to use the fact that $\sqrt{x^2+y^2}\geq\frac{x+y}{2}.$ $$$$ I have ... limits multivariable-calculus derivatives- 59
Prove $f(x,y) = x^4+x^2y +y^2$ has a minimum at $(0,0)$. [closed]
Prove $f(x,y) = x^4+x^2y +y^2$ has a minimum at $(0,0)$. I tried using the second partial derivative test but the results were inconclusive, any help will be useful . multivariable-calculus maxima-minima- 1
Intersection between algebraic curves and its asymptotes
I have been studying the intersection of algebraic curves and asymptotes from the book Taneja, H. C. (2010). Advanced Engineering Mathematics. According to the author, If an Nth degree algebraic ... real-analysis multivariable-calculus algebraic-geometry algebraic-curves- 21
Baby Rudin theorem 11.42
There are the definitions which we need for the proof of the theorem : There is the theorem: If ${f_n}$ is a Cauchy sequence in $\mathscr L^2(\mu)$ , then there exists a function $f$ $\in$ $\mathscr ... integration functional-analysis measure-theory multivariable-calculus cauchy-sequences- 395
Differentiability of $g(x,y) := f \left(\sqrt{x^{2} + y^{2}}\right)$
Suppose the function $f : \Bbb R \to \Bbb R$ is continuously differentiable and define another function $g$ as $$g(x,y) := f \left(\sqrt{x^{2} + y^{2}}\right)$$ Under what condition is $g$ ... real-analysis multivariable-calculus derivatives scalar-fields- 169
Finding a volume using a double integral
Problem: Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola $y = 4 - x^2$ and the line $y = 3x$, while the top of the solid is bounded by the plane $... calculus integration multivariable-calculus volume- 3,128
Can the Jacobian change sign when integrating by substitution?
I'm studying calculus with the textbook "Calculus" by James Stewart. I was curious about the sign of the Jacobian when a change of variables occurs. Inside the text's boundary, there doesn't ... integration multivariable-calculus jacobian- 11
Difficulty computing volume enclosed by parametrized surface $x=\frac{t^2}{1+t^3},y=\frac {t\cos\phi}{1+t^3},z=\frac {t\sin\phi}{1+t^3} $
Compute the volume of the solid $V$ enclosed by the surface $x(t,\varphi)=\frac{t^2}{1+t^3},y(t,\varphi)=\frac{t}{1+t^3}\cos\varphi,z(t,\varphi)=\frac{t}{1+t^3}\sin\varphi, t\in[0,+\infty),\varphi\in[... integration multivariable-calculus divergence-theorem- 41
Calculate total derivative directly.
Calculate directly (not via partial differentiation) the total derivative of the function $f(x_1,x_2)=x_1^2-10x_2.$ You may wish to use the fact that $\sqrt{x^2+y^2}\geq\frac{x+y}{2}.$ $$$$ For the ... limits multivariable-calculus derivatives multivalued-functions- 59
Calculating integral of function over group blocked by lines
I cant seem to find an online tool to help calculate these kind of integrals in order to confirm weather my solution is correct/incorrect, the problem is such: Let $Q$ be the group representing the ... multivariable-calculus change-of-variable fubini-tonelli-theorems- 163
Why we do care about open/closed regions in math - specifically in multivariable calculus? [closed]
I am studying multivariable calculus and I have encountered the idea of an open/unbounded vs closed/bounded region. I understand this is similar to the concept of interval notation where $(5,5)$ does ... multivariable-calculus- 92
Finding Curvature, is $K=\frac{|\vec{s}'(t) \times \vec{s}''(t)|}{||\vec{s}'(t)||^3}$ the right formula to use?
In this lesson, Grant/Khan taught that $K=\frac{|\vec{s}'(t) \times \vec{s}''(t)}{||\vec{s}'(t)||^3}$: = If the formula is right, is it generalisable to all dimensions? I applied it to $\vec{s}(t)= (\... calculus linear-algebra multivariable-calculus curvature- 655
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