12.8.2 Greatest hits from previous weeks

12.8.2.1 Finding unit tangent, normal, and binormal vectors for a given r(t)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18598

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. 
 
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ... 
[equation-solving] [calculus-and-analysis] [geometry] [vector-calculus] [homework]
 

asked by a98 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5605 Score of 33

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 Score of 48

12.8.2.2 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 88

12.8.2.3 Conversion of Sine to Cosine

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=67521

I'm solving equations with many Cosines and Sines. 
And I want to convert all the Sines to Cosines using trigonometric formulas such as cos(x)=sin(x+pi/2). 
How can I do this? 
[trigonometry] [conversion]
 

asked by YongCheol Kwon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=23041 Score of 6

answered by Sjoerd C. de Vries https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=57 Score of 2

12.8.2.4 What does # mean in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19035

I asked Mathematica to compute the following 
 
 Solve[c (1-x)^2-x^(1/4) == 0, x] 
 
 
and it returned this: 
x = Root[#1^8 c^4 - 8 #1^7 c^4 + 28 #1^6 c^4 - 56 #1^5 c^4 +... 
[syntax] [core-language]
 

asked by ronanymous https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5730 Score of 53

answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 Score of 82

12.8.2.5 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

12.8.2.6 Mathematica Minecraft

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19669

Some time ago I asked myself: with all these great graphics and interactive capabilities of Mathematica, what kinds of 3D games can be implemented in it?  And the answer which came to mind is ... 
[programming] [dynamic] [graphics3d] [eventhandler] [development]
 

asked by faleichik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=219 Score of 174

answered by faleichik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=219 Score of 257

12.8.2.7 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 Score of 2

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