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How well can Mathematica do multivariate intergrating

Posted 10 years ago
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Dear Community,

At the moment I'm using Maple, however i'm not satisfied by the way it does multivariate integration and I'm wondering if I should switch to Mathematica.

Could someone tell me how Mathematica would deal with this simple example problem:
A typical example (from gaussian beam optics) is to find the normalization constant N for
$E(x_1)=N exp[-ik x^T Q x ]$
using the conservation of energy
1/N=$\int \int E(x_1) E(x_1)^* dx_1dy_1$
where $*$ is complex conjugation,$Q \el R^{4x4}$ and has the property that $Q=Q^T$ and $x=[x_1 y_1 x_2 y_2 ]$.

Thanks!
Kind regards,
Carlas
POSTED BY: Mr Burns
3 Replies
Multivariate integration by itself is no big deal.  Examples are scattered through
   http://reference.wolfram.com/mathematica/ref/Integrate.html

In[6]:= Integrate[ Sin*Sqrt, x, y]

Out[6]=  
    2      3/2
- ( - )  y         Cos
    3

In[7]:= Integrate[ Sin[x*Sqrt], x, y]

Out[7]=  
   2 Sin[x Sqrt]
-(   ----------------   )
            x
POSTED BY: Bruce Miller
Could you translate the notation into something that does not assume as much background?
POSTED BY: Bruce Miller
Posted 10 years ago
Correction: $E(x_1)=N \int \int E_0(x_2) exp[-ik x^T Q x ]dx_2dy_2$
POSTED BY: Mr Burns
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