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Joe
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10 votes
5 answers
2k views

Confusion in fundamental theorem of calculus

8 votes
2 answers
592 views

If $\vec{\nabla} \cdot \vec{V} \neq 0$ at only one point, will this prevent us from saying that $\vec{V}=\vec{\nabla} \times \vec{U}$?

8 votes
1 answer
238 views

The integral is not iterated integral. Will this fact prevent us from swapping the order of surface and volume integrals? Why? Why not?

7 votes
2 answers
752 views

How much rigour is this proof of multivariable chain rule?

5 votes
4 answers
402 views

Proof that $\sqrt{2}$ is irrational is not convincing. Please help.

4 votes
1 answer
297 views

Is orientation of Stokes theorem a convention?

4 votes
3 answers
912 views

How to change the order of integration when limit is a function?

4 votes
4 answers
2k views

Rigorous proof of surface area formula

4 votes
1 answer
185 views

Can we allow $f$ to be undefined at finitely many points in $(a,b)$ when formulating $\int_a^b f(x)\ dx=F(b)-F(a)$, ($F$ is the antiderivative of $f$)

4 votes
0 answers
284 views

Is Leibniz integral rule (basic form) allowed in this (physics) improper integral? Why?

4 votes
1 answer
193 views

How to prove the limit exist?

4 votes
0 answers
460 views

Divergence theorem: Simple solid region OR compact region and piecewise smooth boundary

4 votes
2 answers
1k views

Definite integral integration by parts

3 votes
4 answers
4k views

Why can't all vector functions not be gradient of a scalar function?

3 votes
3 answers
101 views

Confusion in direction of differentiation

3 votes
0 answers
57 views

Please explain how the following derivative graphically makes sense.

3 votes
3 answers
5k views

difference between tending to zero and close to zero

3 votes
2 answers
283 views

Why is it contradicting?

3 votes
1 answer
388 views

Showing volume and surface integration is unaffected by the singularity at $\mathbf{r'}=\mathbf{r}$

3 votes
0 answers
101 views

Why is electric potential function in free space infinitely differentiable?

3 votes
1 answer
279 views

Is my interpretation of three dimensional improper integral correct?

3 votes
2 answers
855 views

Confusion in least upper bound axiom

3 votes
5 answers
219 views

Can we deduce two contradictory statements from a wrong statement? [duplicate]

3 votes
1 answer
699 views

Is divergence theorem applicable for improper integrals?

2 votes
2 answers
113 views

What are the unknown steps to show $\mathbf{F}=-\nabla\psi$?

2 votes
1 answer
284 views

Can one always interchange the order of a surface and volume integral?

2 votes
1 answer
223 views

How to deal with constants when equating two potential energies?

2 votes
0 answers
125 views

Why are we not using Dirac delta and ignoring the contribution to the surface integral from the point $r=0$?

2 votes
0 answers
38 views

Under what conditions are partial derivatives continuous?

2 votes
1 answer
223 views

How to prove the integral converges?