# 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?