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• Tangent bundles
  The total work over a path in the complex is the ''line integral''<!--\index{line integral}--> of $\varphi$ over a $1$-chain $a$ in $K$. It is simply the sum ...system, $(dx,dy)$ and the best affine approximation (given by the tangent line) becomes a linear function in this system:
  16 KB (2,753 words) - 13:55, 16 March 2016
• Calculus with Analytic Geometry III -- Spring 2014
  ...s in dimension 2 and 3: parametric curves, functions of several variables, line, surface, and volume integrals, some vector calculus ''Chapter 16: Line and Surface Integrals''
  5 KB (621 words) - 14:57, 5 May 2014
• Vector functions
  &= ( 1 + 2b, 3 + b ) + t ( -1, -2 ) {\rm \hspace{3pt} (straight \hspace{3pt} line).} In [[Calc 1]], the answer is "[[tangent line]]'" for functions of one variable. Same for [[parametric curves]]. For [[fu
  28 KB (4,769 words) - 19:42, 18 August 2011
• Linear operators: part 4
  *${\bf R}^3 \rightarrow {\bf R}^1$, or any line. "The [[horizontal line test|horizontal plane test]]", i.e., more than one intersection implies the
  13 KB (2,067 words) - 01:11, 12 September 2011
• Measuring the volume of prostate cancer tumor
  <p>Next, the tumor. The dotted line is made solid using MS Paint. The you run Pixcavator. The [[contour]] has t ...rms this number. Of course, the error can be easily cut down by making the line 1/2 thinner… To be fair the error should be divided by 2.</p>
  6 KB (1,020 words) - 15:01, 21 May 2011
• Metric complexes
  The arc-length is an example of a ''line integral''<!--\index{line integral}--> of a $1$-form $\rho$ over a $1$-chain $a$ in complex $K$ equip What's left? The complex $K$ must be a complex representation of the infinite line or the circle:
  35 KB (5,871 words) - 22:43, 7 April 2016
• Metric tensor
  The arc-length is an example of a ''line integral''<!--\index{line integral}--> of a $1$-form $\rho$ over a $1$-chain $a$ in complex $K$ equip What's left? The complex $K$ has to be a complex representation of the line or the circle:
  42 KB (7,131 words) - 17:31, 30 November 2015
• Seurat's painting
  ...ge. Much less noise and, in addition to the sail, the leaves and the shore line are captured too. So, the bottom line is you can't rely entirely on contrast/persistence and ignore [[measuring o
  3 KB (413 words) - 18:32, 7 January 2011
• Calculus 3: test 1
  3. Find the plane through the origin perpendicular to the line from $(1,0,0)$ and $(0,1,1)$. 5. Find the line tangent to the curve
  799 bytes (132 words) - 15:21, 9 March 2014
• Maps of polyhedra
  ...izations $|g|,|h|:X \to Y$ of these simplicial maps, they will be straight-line homotopic: ...Why can't we simply use for $G$ a simplicial approximation of the straight-line homotopy $F$?
  51 KB (9,162 words) - 15:33, 1 December 2015
• Chain complexes
  Dimension $0$ (no change in the first line): Dimension $1$ (no change in the first line):
  33 KB (5,293 words) - 03:06, 31 March 2016
• Continuous vs discrete differential forms
  It's like the second line is a grainy image of the real life in the first line. How is this image made and how much information does it preserve.
  9 KB (1,483 words) - 13:54, 13 April 2013
• Simplicial complexes
  ...nse that if you throw three points on the plane, the probability that they line up is zero. They are also called “geometrically independent”. ...w values of $r$, construct the Vietoris-Rips complex for: four points on a line, or at the corners of a square, five points at the corners of a pentagon, f
  30 KB (5,021 words) - 13:42, 1 December 2015
• Calculus III -- Fall 2017 -- final
  ...d the directional derivative of the function above in the direction of the line $y=x$. $\bullet$ '''4.''' Sketch the vector field given below and estimate its line integral along the boundary of the square oriented counterclockwise (multip
  2 KB (260 words) - 17:29, 11 December 2017
• Midtearm
  ...Find the line passing through the point $(-1,2)$ and perpendicular to the line $y=-x-2016.$
  2 KB (308 words) - 15:23, 2 March 2016
• Cubical complex
  Dimension $0$ (no change in the first line): Dimension $1$ (no change in the first line):
  29 KB (4,800 words) - 13:41, 1 December 2015
• Solving systems of linear equations
  The line is important! It reminds you: ''augmented matrix is not a matrix''. ...set is $S = \{ x = a+tv \colon t \in {\bf R} \}$. By definition, $s$ is a line:
  5 KB (802 words) - 01:38, 6 September 2011
• Calculus I -- Fall 2016
  **Number systems. Distance formula. Slope of a line. Standard equations of lines. ...nition of the derivative at a point and on an interval. Slope of a tangent line. Derivatives of polynomials. Derivatives of trigonometric functions. Deriva
  11 KB (1,671 words) - 23:11, 13 December 2016
• Elementary Linear Algebra -- Spring 2018 -- midterm
  $\bullet$ '''2.''' In an effort to find the line in which the planes $ 2x -y- z=2 $ and $-4x+2y+2z=1$ intersect, a student $\bullet$ '''5.''' Find the vector equation of the line parallel to both $xy$- and $xz$- coordinate planes and passing through $(2,
  2 KB (308 words) - 23:06, 14 March 2018
• Cubical complexes
  Dimension $0$ (no change in the first line): Dimension $1$ (no change in the first line):
  20 KB (3,319 words) - 14:18, 18 February 2016

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