0
votes
1answer
62 views

Compatibility Condition of the Poisson Equation with Neumann Boundary Conditions

I am trying to solve the following general Poisson equation with homogeneous Neumann boundary conditions in a rectangular domain ($0 \le x \le L$ and $0 \le y \le H$). $$ \frac{\partial^2 ...
0
votes
0answers
65 views

What is a transform?

I've been working in vain to find a way to find the integral of an intractable function. It's great practice anyway. I thought about using intergration by parts with three functions to solve it and ...
1
vote
1answer
82 views

Change of variables in double integral - what's wrong?

I have a homework problem, as follows: Evaluate the double integral by making an appropriate change of variables. $\iint_R 9\sin(49x^2+16y^2)\,dA$, where $R$ is the region in the first ...
1
vote
1answer
36 views

Does the transformation $x=Pabc$, $y=Qab(1-c)$, $z=Ra(1-b)$ map a unit cube to a tetrahedron?

Does the transformation $x=Pabc$, $y=Qab(1-c)$, $z=Ra(1-b)$ map a unit cube in $abc$ coordinates to the tetrahedron with vertices $(P,0,0)$, $(0,Q,0)$, $(0,0,R)$ and $(0,0,0)$ in xyz coordinates? ...
0
votes
1answer
163 views

Find a transformation from tetrahedron to cube in $R^3$ to calculate a triple integral?

I would like to calculate the triple integral of a function $f(x,y,z)$ over a region given by a tetrahedron with vertices $(0,0,0)$, $(a,0,0)$, $(0,b,0)$ and $(0,0,c)$. I am trying to do this by ...
1
vote
1answer
128 views

Evaluating part of a triple integral by changing from rectangular coordinates to cylindrical coordinates

Seeing that this is my first time posting, I hope I'm following the rules correctly. Anyways, the question I'm stuck on is: Evaluate: $$ \int_{-3}^3\int_{-2}^2\int_{-\sqrt{9-y^2}}^\sqrt{9+y^2} ...
5
votes
4answers
135 views

Change of variables Double integral

I have $$\iint_A \frac{1}{(x^2+y^2)^2}\,dx\,dy.$$ $A$ is bounded by the conditions $x^2 + y^2 \leq 1$ and $x+y \geq 1$. I initially thought to make the switch the polar coordinates, but the line ...
0
votes
1answer
119 views

Question about L2 Inner Product and Integrals

Does exists $f\in L_2(\mathbb{R}^d)$ such that for all $g\in L_2(\mathbb{R}^d)$ which is not identically zero: ...
3
votes
0answers
59 views

Can I solve for a unique integral kernel?

Consider, for $\mathbf{v},\mathbf{w} \in \mathbb{R^3}$, $$ f(\mathbf{w}) := \int K(\mathbf{w,\mathbf{v}}) g(\mathbf{v}) \, d\mathbf{v} \, .$$ Is it possible to solve for the integral kernel, ...