# Search results

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?
16. ### Multiplicity of a pole

May this be extended beyond polynomials?
17. ### Multiplicity of a pole

For f(z)=\frac{1}{(z-z_0)^n}, the pole at z=z_0 has multiplicity n
18. ### Integrate (x^3 + x^2)/(1 + x^4) using substitution?

Your fractions should be of the form: \frac{Ax+B}{1-x\sqrt{2}+x^{2}} + \frac{Cx+D}{1+x\sqrt{2}+x^{2}}.
19. ### Integrate (x^3 + x^2)/(1 + x^4) using substitution?

1+x^4 = 1+2x^2+x^4 - 2x^2=(1+x^2)^2-2x^2=(1-\sqrt 2 x + x^2)(1+\sqrt 2 x+x^2). As to partial fraction decomposition, I suggest you have a look in your textbook or at wikipedia or other webpages.
20. ### Integrate (x^3 + x^2)/(1 + x^4) using substitution?

I have not tried this, but you could try factoring 1+x^4 into two quadratics, then do partial fraction decomposition.
21. ### I need help in a problem

Alright, thanks!
22. ### I need help in a problem

Why not "guess" a solution of the form x^r, and end up with solutions x^{1/2 \pm i\sqrt{3}/2}, which are essentially the same as Crosson ended up with?
23. ### Periodic question?

Is it possible to construct an example x = f(x)+g(x), where f and g are periodic functions?
24. ### Hermite Polynomials.

What two other conditions do these polynomials have to satisfy?
25. ### Hermite Polynomials.

e^{-y^2}=\sum_{n=0}^{\infty}\frac{(-y)^{2n}}{n!} Is this correct? I'm inclined to think that: e^{-y^2}=\sum_{n=0}^{\infty}\frac{(-y^2)^{n}}{n!} =\sum_{n=0}^{\infty}\frac{(-1)^n y^{2n}}{n!}.?
26. ### Prove the integral

You could also do this by partial fraction decomposition.
27. ### Derivative proof with a fractional exponent

I agree, sorry.
28. ### Derivative proof with a fractional exponent

Kurret: This is not the concept discussed, you have taken the first derivative of some function. The topic is fractional derivatives (for example: what does it mean to take the pi'th derivative of a function?) not the derivatives of functions of fractional powers.,
29. ### Derivative proof with a fractional exponent

Would you care to elaborate on that, HallsofIvy?
30. ### Integral of x^{2} e^{-x^2} dx

Quite frankly, I think using Leibniz' rule, as suggested by Nicksauce, would by far be the simplest method in this case.