Recent content by jasonmcc

$ kxy \frac{dy}{dx} = y^2 - x^2 \quad , \quad y(1) = 0 $ My professor suggests substituting P in for y^2, such that: $ P = y^2 dP = 2y dy $ I am proceeding with an integrating factor method, but unable to use it to separate the variables, may be coming up with the wrong integrating factor ( x )

I haven't done ODEs in a while nor have a book handing. How do I tackle an equation of the form \[ 2xyy'=-x^2-y^2 \] I tried polar but that didn't seem to work.

Thanks for all the help and action! I was traveling and away from my computer; great to see the discussion.

Homework Statement Given a cylinder in the Ox1x2x3 coordinate system, such that x1 is in the Length direction and x2 and x3 are in the radial directions. The stress components are given by the tensor $$ [T_{ij}] = \begin{bmatrix}Ax_2 + Bx_3 & Cx_3 & -Cx_2 \\ Cx_3 & 0 & 0 \\ -C_2 & 0 &...

Yes nevermind I was looking at your solution backwards. Breaking up $A_{(ij)}B_{[ij]} + A_{[ij]}B_{(ij)}$ into elements it all canceled out except $$ \frac{1}{2}(A_{ij}B_{ij} - A_{ji}B_{ji}) $$ so if that equals zero we are good...

Dustin, I think you basically solved it in line 1, since $$ A_{ij} = A_{(ij)} + A_{[ij]} $$ (decomposition of the tensor into symmetric $(A_{(ij)}$ and antisymmetric $(A_{[ij]})$ parts), so $$ A_{ij}B_{ij} = (A_{(ij)} + A_{[ij]})(B_{(ij)} + B_{[ij]}) $$ But how does $$ A_{(ij)}B_{(ij)} +...

there is an easier way, of course, using indicial. $$ \mathcal{A}_{mi}\varepsilon_{mjk} + \mathcal{A}_{mj}\varepsilon_{imk} + \mathcal{A}_{mj}\varepsilon_{ikm} = \mathcal{A}_{mk}\varepsilon_{ijk}\\ $$ multiplying all by $\varepsilon_{ijk}$ leads to kroniker delta rules, whereupon the expression...

Use indicial notation to show that: $$ \mathcal{A}_{mi}\varepsilon_{mjk} + \mathcal{A}_{mj}\varepsilon_{imk} + \mathcal{A}_{mk}\varepsilon_{ijm} = \mathcal{A}_{mm}\varepsilon_{ijk} $$ I'm probably missing an easier way, but my approach is to rearrange and expand on the terms: $$...

Thanks. What do you think they mean by "Expand", then?

Hi, I'm working on a problem stated as: Expand the following expression and simplify where possible $$ \delta_{ij}\delta_{ij} $$ I'm pretty sure this is correct, but not sure that I am satisfying the expand question. I'm not up to speed in linear algebra (taking a continuum mechanics course) -...