8.7.2 Greatest hits from previous weeks

8.7.2.1 Plotting a Phase Portrait
8.7.2.2 What does # mean in Mathematica?
8.7.2.3 1 Plot, 2 Scale/Axis
8.7.2.4 Make a scatter plot from two lists
8.7.2.5 Finding unit tangent, normal, and binormal vectors for a given r(t)
8.7.2.6 How can I transpose x and y axis on a Plot?
8.7.2.7 How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?
8.7.2.1 Plotting a Phase Portrait

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=14160

I'm trying to plot a phase portrait for the differential equation 
$$x'' - (1 - x^2) x' + x = 0.5 \cos(1.1 t)\,.$$ 
The primes are derivatives with respect to $t$. I've reduced this second order ODE to ... 
[plotting] [differential-equations]
 
asked by covertbob https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4528 Score of 41
answered by David Slater https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1746 Score of 39
8.7.2.2 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 43
answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 Score of 74
8.7.2.3 1 Plot, 2 Scale/Axis

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=627

I would like to plot those two datasets on top of each other. But they have very different range on the $y$ axis. How can I have two different axis? 
 
I found the following on the help menu but quite ... 
[plotting] [customization]
 
asked by 500 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=172 Score of 156
answered by ArgentoSapiens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=92 Score of 158
8.7.2.4 Make a scatter plot from two lists

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=21884

I have two lists of values 
 
 xx = {0.1, 0.3, 0.35, 0.57, 0.88, 1.0} 
yy = {1.2, 3.5, 4.5, 7.8, 9.0, 12.2} 
 
 
I want to make a scatter plot (list plot) with xx as x ... 
[plotting]
 
asked by JACKY Li https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2403 Score of 28
answered by Eric Thewalt https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=6313 Score of 42
8.7.2.5 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 32
answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 Score of 47
8.7.2.6 How can I transpose x and y axis on a Plot?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18655

This question has appeared in various forms online, but I have not yet seen a complete answer, so I am posting it here. 
 
More specifically, suppose I have a function 
 
... 
[plotting] [graphics]
 
asked by merlin2011 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5619 Score of 16
8.7.2.7 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,... 
[symbolic] [physics] [tensors] [differential-geometry]
 
asked by Zoe Rowa https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1713 Score of 47
answered by Yi-Zen Chu https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4869 Score of 23