/sci/ - Science & Math

>>11359616
Bundle Fumble by Bob Mundell.
Literally any "geometry for physics" or "differential geometry for physics" book. Physicists love bundles.
There's also Tu's Differential Geometry, that one's good.
But what you should do is learn the differential geometry of curves and surfaces.

>>11301569
>why is [math][f+g]_R[/math] is integrable
For [math]f, g[/math] nonnegative, we have [math][f+g]_R=[[f]_R+[g]_R]_R[/math].
If you have that [math][f]_R[/math] is integrable when [math]f[/math] is, the rest should be immediate.
>>11301575
[math]Au=v[/math]. We write out [math]A[/math] as the sequence of rows [math]A_i[/math].
Then, the i-th term of [math]v[/math] is [math]\langle A_i ^T, u \rangle[/math]. Thus, if [math]v[/math] is everywhere zero, [math]\langle A_ i ^T, u \rangle = 0[/math].