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• 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
• Lengths of curves
  If r is the size of the pixel, a line segment of length a will be represented by roughly $a/r$ pixels… but only ...] of a curve is ''defined'' and computed via approximation of the curve by line segments. The difference is that the end points of these segments lie ''exa
  13 KB (2,113 words) - 20:21, 7 February 2013
• Calculus exercises: part II
  *A chord of a circle is a straight line segment whose end-points lie on the circle. Find the average length of a ch *Given a parametric curve $x=\sin t,\ y=t^2$. Find the line(s) tangent to the curve at the origin.
  15 KB (2,591 words) - 17:15, 8 March 2018
• Combinatorial cell maps
  '''Example.''' This projection of a triangle on a line segment is not a cell map: ...system, $(dx,dy)$ and the best affine approximation (given by the tangent line) becomes a linear function in this system:
  31 KB (5,330 words) - 22:14, 14 March 2016
• Products
  ...dance” in robotics by constructing such a “safe” configuration space. On a line segment, this configuration space of three robots will be a cube with three '''Exercise.''' Find the safe configuration space for two robots on a line, the circle, the tripod. What if they are connected by a rod? a rope?
  44 KB (7,951 words) - 02:21, 30 November 2015
• Discrete functions
  ...$f$ -- a discrete function $g$ defined at predetermined points of the real line. What is its derivative? ...valuated at one of the intervals rather than points -- is the slope of the line that connects the endpoints of the segment.
  15 KB (2,532 words) - 12:21, 11 July 2016
• Linear operators: part 1
  ...is the projection, $X = {\bf R}^2$, $Y=x$-axis, $f^{-1}(c)$ is a vertical line, $f^{-1}(B)$ is the strip: The fist line is just the two functions "wired together" but the second is more revealing
  13 KB (2,086 words) - 19:58, 27 January 2013
• Calculus of discrete differential forms
  So, on $\alpha$, using [[antisymmetry]] to get the third line, Of course we recognize this as a [[line integral]]. We can read this as follows:
  9 KB (1,503 words) - 18:30, 22 August 2015

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