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• Differential Forms: A Complement to Vector Calculus by Weintraub
  The integral of a 1-form over a curve ([[line integrals]]) The [[fundamental theorem of calculus]] and its analog for line integrals
  2 KB (249 words) - 19:55, 6 October 2016
• Using derivative to find extreme values
  Recall, $f^{\prime}(c)$ is the [[limit]] of [[slope]]s of the [[secant line]]s. Take any (secant) line through $(x, f(x))$ and $(c,f(c)), x < c$. Then
  6 KB (1,041 words) - 15:17, 12 July 2011
• Calculus I -- Spring 2017
  **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
  12 KB (1,803 words) - 20:50, 1 May 2017
• Geometry
  The arc-length is an example of a ''line integral'' of a $1$-form $\rho$ over a $1$-chain $a$ in complex $K$ equippe What's left? The complex $K$ has to be a complex representation of the line or the circle:
  41 KB (6,928 words) - 17:31, 26 October 2015
• Diffusion
  The answer is, of course, Yes. If we assume that the liquid flows along the line (the pipe $a^\star$) that connects the centers of the rooms, then what matt ...borhood is the Hodge dual of this point. We recognize this expression as a line integral:
  39 KB (6,850 words) - 15:29, 17 July 2015
• Integration
  In the graph, $dx$ is the run and $dy$ is the rise of the tangent line. They are called the ''differentials'' of $x$ and $y$ respectively. The dep We also define the integral over the whole real line $(-\infty,\infty)$ in terms of the ones over rays, as the sum of two corres
  69 KB (11,727 words) - 03:34, 30 January 2019
• Calculus I -- Spring 2017 -- final
  $\bullet$ '''3.''' Use implicit differentiation to find an equation of the line tangent to the curve $x^{1/2}+xy=2$ passing through the point $(1,1)$. $\bullet$ '''4.''' Find the point on the line $y=1-2x$ that is closest to the origin.
  1 KB (233 words) - 03:04, 2 May 2017
• Homotopy and homotopy equivalence
  This is called the ''straight-line homotopy''. ...ply connected because every loop can be deformed to a point via a straight line homotopy:
  45 KB (7,738 words) - 15:18, 24 October 2015
• Partial derivatives
  and the slope of the tangent line is $\frac{\partial f}{\partial x}_1(a)$, which is the derivative of $z = f and the slope of the tangent line is $\frac{\partial f}{\partial x_2}(a)$.
  3 KB (547 words) - 21:22, 28 August 2011
• Directional derivative
  ...ws the given direction. The point $a$ and the vector $e$ together define a line (a $1$-dimensional [[affine subspace]]) $L$: which is the slope of the [[tangent line]] to the curve at this point.
  4 KB (715 words) - 20:12, 28 August 2011
• Integration of differential forms of degree 0 and 1
  Let's review [[line integral]]s ([[Calculus 3: course|calc 3]]) first. The line integral along $C$ (with respect to this parametrization), is, as an exampl
  12 KB (1,906 words) - 17:44, 31 December 2012
• Calculus by Stewart
  [[Vector fields]]. [[Line integrals]]. [[The fundamental theorem for line integrals]]. [[Green's theorem]]. [[Curl]] and [[divergence]]. [[Parametric
  6 KB (794 words) - 16:29, 13 August 2017
• Image analysis software
  | graphical applications (GUI) and a set of command-line utilities ...ou to easily develop custom image analysis macros without writing a single line of code
  8 KB (1,135 words) - 14:48, 4 November 2011
• Precalculus with Scientific Applications -- Spring 2016 -- midterm
  ...Find the line passing through the point $(-1,2)$ and perpendicular to the line $y=-x-2016.$
  2 KB (308 words) - 17:21, 2 March 2016
• Discrete differential forms
  What if we choose, for $g'$, [[secant line]]s instead of [[tangent line]]s?
  10 KB (1,471 words) - 12:50, 12 August 2015
• Grayscale images - implementation
  |<font color=#0000FF><u>GetMinLine()</u></font>||Retrieves min line integral.
  13 KB (2,095 words) - 16:48, 4 December 2009
• Calculus 1: test 1
  ...$a=1$ from the definition (i.e., as a limit). (b) Find the equation of the line tangent to the graph of $y=f(x)$ at the point corresponding to $a=1$.
  2 KB (255 words) - 20:22, 13 June 2011
• Vector calculus: exam 2
  7. Find the tangent line to the curve $f(t)=(t,t^2,t^3)$ at the point $(1,1,1)$.
  1 KB (190 words) - 02:41, 22 August 2011
• Character recognition
  ...on of the location of [[center of mass]] of the letter with respect to the line, its [[size]], and its [[Topological Features of Images|topology]] allows y
  843 bytes (116 words) - 14:08, 7 October 2010
• Calculus I -- Fall 2017 -- midterm
  ...''3.''' The graph of a function $f$ is given below. Find the equation of a line tangent to the graph at $(0,-1)$.
  1 KB (246 words) - 14:16, 29 October 2018

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