6.6.2 Greatest hits from previous weeks

6.6.2.1 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot  ... 
[calculus-and-analysis] [series-expansion]
 

asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 55 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 61 votes

6.6.2.2 How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=8895

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes, I run into the following error: 
 
 
... 
[tensors] [differential-geometry]
 

asked by Zoe Rowa https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1713 36 votes

answered by Yi-Zen Chu https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4869 17 votes

6.6.2.3 How to create effect like Van Gogh's stroke brush?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=39003

I need to apply Van Gogh's stroke brush effect to a random image 
 
 
Take the following image as an example: 
 
Thank you so much if you could help! 
 
[image-processing] [code-request] [generative-art]
 

asked by user10495 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=10495 33 votes

answered by Simon Woods https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=862 51 votes

6.6.2.4 How to perform a multi-peak fitting?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=26336

I am wondering how to implement the multi-peak detecting and fitting in Mathematica. Following is an example of fitting the data using three peaks (such that the data ~ peak1 + peak2 + peak3). 
 
 
 
The  ... 
[fitting] [data] [peak-detection]
 

asked by Everett You https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1389 54 votes

answered by Silvia https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=17 54 votes

6.6.2.5 What are the most common pitfalls awaiting new users?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18393

As you may already know, Mathematica is a wonderful piece of software. 
However, it has a few characteristics that tend to confuse new (and sometimes not-so-new) users. That can be clearly seen from  ... 
[programming] [core-language] [faq] [guidelines]
 

asked by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 460 votes

answered by Michael E2 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4999 277 votes

6.6.2.6 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

6.6.2.7 $\LaTeX$ and Mathematica

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=736

I quite often would like to draw graphics in my $\LaTeX$ documents using Mathematica. I have encountered three problems. I would like to know if there are any workarounds to these problems 
 
I would  ... 
[graphics] [export] [latex]
 

asked by Thomas Rot https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=227 124 votes

answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 45 votes