10.40.2 Greatest hits from previous weeks

10.40.2.1 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 \nabla)... 
[calculus-and-analysis] [series-expansion]
 

asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 Score of 77

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 Score of 87

10.40.2.2 How to ask Mathematica to imitate Andy Warhol's pop-art painting?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=59132

I tried to ask Mathematica to imitate Andy Warhol, let it convert a Marilyn Monroe's portrait so that it looks like Warhol's world famous pop-art painting. However, the result shown below is far from ... 
[image-processing] [generative-art]
 

asked by Putterboy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=16069 Score of 53

answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 Score of 68

10.40.2.3 Are you interested in purchasing David Wagner's "Power programming with Mathematica"?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=16485

I recently contacted McGraw-Hill to see if they have a mechanism in place for printing out-of-print books that are still of interest.  Specifically, I asked about "Power programming with Mathematica" ... 
[reference-request]
 

asked by Todd Allen https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=249 Score of 165

10.40.2.4 Extract real part of a complex expression better than Re does

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3306

I have a complex expression with real positive variables only. 
 
Mathematica Input Style: 
 
... 
[symbolic] [trigonometry]
 

asked by max https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=796 Score of 39

answered by nixeagle https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=814 Score of 62

10.40.2.5 How to express trigonometric equation in terms of of given trigonometric function?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=434

How can I express a trigonometric equation / identity in terms of a given trigonometric function? 
 
using following trigonometric identities 
 
... 
[functions] [trigonometry]
 

asked by Prashant Bhate https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=99 Score of 31

answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 Score of 38

10.40.2.6 How to add a vertical line to a plot?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3561

In the plot below I would like to add two vertical lines at $x = \frac{\pi}{15} \pm \frac{1}{20}$. 
How can I do that? 
 
... 
[plotting]
 

asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 Score of 87

answered by Ajasja https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=745 Score of 102

10.40.2.7 What does "Tag Integer is Protected" message mean?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=6738

(Newbie question) 
 
For every function I define I get this message: 
When I close and reopen Mathematica, and re-enter the function definition, I don't get the message anymore. What does it mean? 
[warning-messages]
 

asked by stevenvh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1450 Score of 16

answered by J. M.'s missing motivation https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 Score of 17