Recent content by Big-T

1. How does one go about proving an elementary solution to an integral does not exist?

How about letting x^x = e^{x\ln x} ?
2. How does one go about proving an elementary solution to an integral does not exist?

http://www.sosmath.com/calculus/integration/fant/fant.html
3. Submersion and fiber bundles

How would one go about to construct a function on (smooth) manifolds that is a submersion without being (the projection map of) a fiber bundle?
4. Contour integration

What contour have you used? Could it have something to with the choice of brance of the square root function?
5. What is sin-1(2i) equal?

For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?
6. Harmonic movement of a spring question

Imagine the unit circle projected onto the y-axis, then pi/4 corresponds to 1, 0 and pi to 0 and -pi/4 to -1 as initial positions.
7. Harmonic movement of a spring question

Your initial conditions gives these equations, from which you should be able to retrieve u: r(t)=Asin(wt+u) r(0)=A
8. Is C bigger than R?

Marcus' function would be well defined if we agreed to use trailing nines wherever the decimal expansion is terminating, this should of course have been specified.
9. Two vector spaces being isomorphic

How many basis vectors do you need to span P_k?
10. Is C bigger than R?

How could that possibly be a bijection? Obviously, z_1=a+ib is mapped to the same point as z_2=a z_1, so it is not an injection. Marcus has already provided a valid bijection, his "decimal merging" is the classical example of this. Notice how it is also valid in \mathbb{R}^n.
11. Need help on this pde

What RedBranchKnight refers to is a special case of the http://en.wikipedia.org/wiki/Method_of_characteristics" [Broken].
12. How is pi derived?

Rudin defines pi/2 to be the smallest positive number such that cos(pi/2)=0.
13. First order pde cauchy problem by method of characteristics

You may have a look here: http://en.wikipedia.org/wiki/Inverse_trigonometric_function#Logarithmic_forms"
14. Multiplicity of a pole

That definition put everything in place, thanks!
15. Multiplicity of a pole

I.e. the multiplicity is the power of the term with the largest negative power in the laurent series of the function? Does this also mean that an isolated/(essential?) singularity is a pole with infinite multiplicity?