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• Motivation for tangent space
  ...ke (informally, because cases where {{M|1=\theta=\tfrac{\pi}{2} }} and {{M|1=r=0}} must be treated carefully) the manifold of the plane. The reader shou * {{M|(r,\theta)\mapsto(r\cos(\theta),r\sin(\theta))}}
  6 KB (975 words) - 00:18, 11 April 2015
• Polar equation of a line
  * {{M|1=y=mx+c}} * <math>r=\sqrt{t^2(m^2+1)+2mtc+c^2}</math>
  1 KB (223 words) - 22:43, 10 April 2015
• Notes:Spherical coordinates
  ...sets of {{M|\mathbb{R}^2}} - we would say the Earth is a ''topological {{M|2}}-manifold''. [[File:Transition map.JPG|thumb|Transition map {{M|\psi\circ\varphi^{-1} }} on a topological {{n|manifold}} {{M|M}}]]
  10 KB (1,899 words) - 18:48, 23 September 2015
• Notes:Tangent space
  * {{M|1=M:=\{p\in\mathbb{R}^3\ \vert\ p=(x,y,x^2+y^2)\}\subset\mathbb{R}^3}} (with the subspace topology) and the two charts: *# {{M|1=i:\mathbb{R}^2\rightarrow M}} by {{M|1=i:(x,y)\mapsto(x,y,x^2+y^2)}} (think of it as like the "identity chart" it is what the manifold is)
  5 KB (1,002 words) - 19:42, 15 August 2016
• Exercises:Mond - Topology - 1/Question 6
  ...for that it sends {{M|-1}} and {{M|1}} to the same point in {{M|\mathbb{S}^1}}. Definitions may be explicit or use a picture ...- 1/Pictures/Q6P1 - 1}}}}We shall define {{M|f:[-1,1]\rightarrow\mathbb{S}^1}} to be such a map:
  7 KB (1,326 words) - 12:26, 12 October 2016
• Example:Smooth map between the real line and the circle (considered as smooth manifolds)
  ...M|\text{Id}_\mathbb{R}:x\mapsto x}}</ref>) and let [[Circle|{{M|\mathbb{S}^1}}]] be considered as a smooth manifold with the smooth structure induced by ...nit length in each direction<ref group="Note">typically we use {{M|I:\eq[0,1]\subset\mathbb{R} }} - say in measure theory, so be aware of that</ref>
  4 KB (757 words) - 13:25, 2 April 2017
• Double angle formulas
  ...n\mathbb{R}[\sin(\varphi\pm\psi)\eq\sin(\varphi)\cos(\psi)\pm\cos(\varphi)\sin(\psi)]}} ...n\mathbb{R}[\cos(\varphi\pm\psi)\eq\cos(\varphi)\cos(\psi)\mp\sin(\varphi)\sin(\psi)]}}
  951 B (155 words) - 18:42, 9 June 2017
• Common integrals table
  {{MM|\newcommand{\plusc}[1][]{ {\ +C#1} } }} * {{MM|\int\text{sin}(x)\mathrm{d}x\eq \cos(x)\plusc{} }}
  805 B (135 words) - 08:11, 11 November 2017
• 2-Dimensional rotation matrix
  * {{M|M:\eq\left(\begin{array}{cc}\cos(\theta)&-\sin(\theta)\\ \sin(\theta)& \cos(\theta)\end{array}\right)}} * {{M|(1,0)^\mathrm{T} \mapsto (\cos(\theta),\sin(\theta))^\mathrm{T} }}, and
  2 KB (315 words) - 08:07, 3 April 2018
• Circular motion
  ...ght]} }}{{M|\newcommand{\dd}[3]{\frac{\mathrm{d} }{\mathrm{d}{#1} }\left[{#2}\right]\Big\vert_{#3} } }}{{Provisional page|grade=A|This and pendulum stuf * {{M|p(t):\eq\Vecc{r(t)\ \!\cos(\theta(t))}{r(t)\ \!\sin(\theta(t))} }} be used for {{M|p}}osition - with respect to time
  2 KB (375 words) - 02:37, 8 April 2018