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  1. B

    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. B

    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. B

    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. B

    Contour integration

    What contour have you used? Could it have something to with the choice of brance of the square root function?
  5. B

    What is sin-1(2i) equal?

    For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?
  6. B

    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. B

    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. B

    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. B

    Two vector spaces being isomorphic

    How many basis vectors do you need to span P_k?
  10. B

    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. B

    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. B

    How is pi derived?

    Rudin defines pi/2 to be the smallest positive number such that cos(pi/2)=0.
  13. B

    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. B

    Multiplicity of a pole

    That definition put everything in place, thanks!
  15. B

    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. B

    Multiplicity of a pole

    May this be extended beyond polynomials?
  17. B

    Multiplicity of a pole

    For f(z)=\frac{1}{(z-z_0)^n}, the pole at z=z_0 has multiplicity n
  18. B

    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. B

    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. B

    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. B

    I need help in a problem

    Alright, thanks!
  22. B

    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. B

    Periodic question?

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

    Hermite Polynomials.

    What two other conditions do these polynomials have to satisfy?
  25. B

    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. B

    Prove the integral

    You could also do this by partial fraction decomposition.
  27. B

    Derivative proof with a fractional exponent

    I agree, sorry.
  28. B

    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. B

    Derivative proof with a fractional exponent

    Would you care to elaborate on that, HallsofIvy?
  30. B

    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.
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