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• Discrete parametric curves
  is also a line but the motion starts at $b \in {\bf R}^n$. [[Image:tangent line examples.jpg|center]]
  32 KB (5,426 words) - 21:57, 5 August 2016
• Preview of calculus: part 1
  ; Answer : We use a tangent line. Why? The tangent line touches the point A and no where else in the curve. If we zoom in, they vir
  10 KB (1,532 words) - 00:07, 2 May 2011
• Convergence of the discrete to the continuous
  ...f the differential equation as a formula by which the slope of the tangent line to the graph of $y$ can be computed at any point on the curve, once the loc ...y the slope of the tangent line of $y$). We take a step along that tangent line up to the next point. We choose a value for the horizontal component of thi
  21 KB (3,664 words) - 02:02, 18 July 2018
• Applications of ODEs
  ...metric curves'' defined at the nodes of the standard partition of the real line: ...he string is found as the negative of the projection of the gravity on the line from $0$ to the current location $X=<x,z>$:
  50 KB (8,692 words) - 14:29, 24 November 2018
• Vector integrals
  ...e $e_1, e_2$ are the (fixed) basis vectors of ${\bf R}^2$. So, if $L$ is a line perpendicular to the square (or a surface), then the orientation is a basis ...]] (on the right) is not good for computing the arc length, but fine for [[line integrals]]: displacement, work, etc. Same applies to [[surface integral]]s
  15 KB (2,545 words) - 19:47, 20 August 2011
• Differential equations
  ...nt line at $(t,y(t))$. This slope is the same along any given ''vertical'' line: ...ent line at $(t,y)$. This slope is the same along any given ''horizontal'' line:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Functions of several variables OLD
  ...to $Q$ for any given $P, Q {\in} {\bf R}^n$. The idea is to use a straight line. In ${\bf R}^m$, we simply replace $|\cdot|$ with $||\cdot||$ in the last line:
  34 KB (5,636 words) - 23:52, 7 October 2017
• Transformations
  That's why there is a whole line of points $X$ with $FX=0$. To find it, we solve this equation: ...ngular stretch-shrink but this time it is between the two ends of the same line. To see clearer, consider what happens to a square:
  46 KB (7,625 words) - 13:08, 26 February 2018
• Limits and continuity
  *3. we think of the function as a ''transformation'' of the real line. ...from Chapter 3: numerical functions are transformations of the real number line... and vice versa.
  107 KB (18,743 words) - 17:00, 10 February 2019
• Linear algebra
  S may be a line... S = (-(3/2)&alpha;, &alpha;, -(1/2)&alpha;) represents a straight line in '''R³'''.
  27 KB (4,667 words) - 01:07, 19 February 2011
• Linear algebra of Euclidean space
  $S$ may be a line... ...ter>$S = (-(3/2) \alpha , \alpha , -(1/2) \alpha )$ represents a straight line in ${\bf R}^3$.</center>
  26 KB (3,993 words) - 19:48, 26 August 2011
• Differential calculus
  ...he most horizontal. In other words, this is where the slope of the tangent line is zero. But that's the derivative of our function. From the ''Power Formul ...words, the monotonicity is determined by the sign of slope of the tangent line. We conclude that on interval $(0,25)$, the derivative is positive and on $
  84 KB (14,321 words) - 00:49, 7 December 2018
• Differentiation
  ...erval, we compute the difference quotients along the two intervals (second line) and place the results at the corresponding edge: ...we carry out the same operation and place the result in the middle (third line).
  82 KB (14,116 words) - 19:50, 6 December 2018
• Calculus I, the discrete version
  We divide the $x$-axis (i.e., the real line ${\bf R}$) into discrete pieces. The ration is also known as the ''slope'' of the line.
  64 KB (11,521 words) - 19:48, 22 June 2017
• Preview of calculus
  ; Answer : We use a tangent line. Why? The tangent line touches the point A and no where else in the curve. If we zoom in, they vir
  4 KB (703 words) - 14:34, 9 September 2016
• Forms in Euclidean spaces
  The simplest example of a differential form is a $1$-form over the real line: ...'s consider its ''discrete'' counterpart. A discrete $1$-form for the real line is, by definition, a collection $\phi$ of linear maps on tangent spaces:
  44 KB (7,778 words) - 23:32, 24 April 2015
• Integer-valued calculus
  ...have a ''hole'' (or tunnel) in it? Is it possible to travel in a straight line and arrive at the starting point from the opposite direction? Like this: ...'simply-connected''. So, if we know all gradients of all functions and all line integrals of all vector fields, we can tell if there is a hole in the regio
  27 KB (3,824 words) - 19:07, 26 January 2019
• Derivative reflects behavior of the function
  [[Image:meanValueTheoremExample.png|right|Movement along a Straight Line]] *The line that connects the end points used to be horizontal and now is has become in
  8 KB (1,470 words) - 00:39, 16 July 2011
• Calculus on cubical complexes
  ...he simplest setting, we deal with the intervals in the complex of the real line ${\mathbb R}$. Then the form assigns a number to each interval to indicate One should recognize the second line as a line integral:
  36 KB (6,218 words) - 16:26, 30 November 2015
• Precalculus exercises
  ...s of the $x$-coordinates of the intersections between the parabola and the line below: [[image:area between parabola and horizontal line.png| center]]
  17 KB (2,933 words) - 19:37, 30 July 2018

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