6.9.2 Greatest hits from previous weeks

6.9.2.1 Is there something like DensityPlot3D to visualize atomic orbitals?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=32378

I'm visualizing some hydrogen like atomic orbitals.  For looking at plane slices of the probability density, the DensityPlot function works well, and with something like: 
 
Manipulate[ 
DensityPlot[  ... 
[plotting] [physics] [chemistry]
 

asked by Peeter Joot https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=10 44 votes

answered by xslittlegrass https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1364 24 votes

6.9.2.2 How to find integer solutions?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=42359

Following is the equation: 
 
 
 
Need to solve for integer values of x,y when a,b lies between -1000 and 1000. 
Problem is to find the number of integer values of pair (x,y) that satisfy it. 
 
[equation-solving]
 

asked by Sahil Sareen https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=12396 2 votes

answered by bill s https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1783 4 votes

6.9.2.3 How can I plot the direction field for a differential equation?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=8841

I'd like to plot the graph of the direction field for a differential equation, to get a feel for it.  I'm a novice, right now, when it comes to plotting in Mathematica, so I'm hoping that someone can  ... 
[plotting] [differential-equations]
 

asked by Matt Groff https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1735 29 votes

answered by Peter Breitfeld https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=307 24 votes

6.9.2.4 Calculate the 2D Fourier transform of an Image

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=29203

I am new to Mathematica, and using version 8.0. 
 
I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase spectrum, as well as reconstruct the  ... 
[image-processing] [image] [fourier-analysis]
 

asked by user8727 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=8727 14 votes

answered by Nasser https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=70 32 votes

6.9.2.5 How do I draw a pair of buttocks?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=66538

I'm trying to develop a function which 3D plot would have a buttocks like shape. 
 
Several days of searching the web and a dozen my of own attempts to solve the issue have brought nothing but two  ... 
[plotting] [graphics3d] [generative-art]
 

asked by Simpleton Jack https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=22399 287 votes

answered by mikuszefski https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7608 440 votes

6.9.2.6 Elegant operations on matrix rows and columns

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3069

Question 
 
The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a  ... 
[list-manipulation] [matrix] [array] [faq]
 

asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 177 votes

answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 60 votes

6.9.2.7 Finding Limits in several variables

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=21544

Is there a way to find a limit of a multivariable function, like 
 
$$\lim_{(x,y)\to (0,0)} f(x,y)$$ 
with Mathematica? 
 
When $f$ is continuous, we can use 
$$\lim_{(x,y)\to (0,0)}  ... 
[functions] [calculus-and-analysis]
 

asked by Dominic Michaelis https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5899 30 votes

answered by whuber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=91 41 votes