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How well can Mathematica do multivariate intergrating

Posted 11 years ago
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 11 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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