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• Calculus of sequences
  ==The real number line== We visualize these as markings on a straight line, according to the order of the planks:
  113 KB (18,425 words) - 13:42, 8 February 2019
• Calculus exercises: part III
  Find a tangent line to the curve parametrized by $f$ at the point $t=2$. ...Therefore, it suffices to simply use $f'(2)$ as a direction vector for the line. Further,
  46 KB (8,035 words) - 13:50, 15 March 2018
• Manifolds
  ...vation that the light from a star passing the sun deviates from a straight line may be considered as evidence in support of this idea: ...arrive to the idea of a locally Euclidean space. The main examples are the line and the circle.
  51 KB (8,919 words) - 01:58, 30 November 2015
• Applications of integral calculus
  ...demonstrated for the special case when such a region is cut by a vertical line: This case is illustrated below (the line is $x=b$):
  103 KB (18,460 words) - 01:01, 13 February 2019
• Systems of ODEs
  *the horizontal line $y=\alpha/\beta$ is crossed vertically by the solutions. *the vertical line $x=\gamma/\delta$ is crossed horizontally by the solutions.
  63 KB (10,958 words) - 14:27, 24 November 2018
• Vector and complex variables
  In fact, either equation is a representations of a line on the plane. Then the solution $(x,y)=(4,2)$ is the point of their interse A ''flip about the line $x=y$'' that appeared in the context of finding the graph of the inverse fu
  113 KB (18,750 words) - 02:33, 10 December 2018
• More on vector spaces
  '''Theorem:''' A straight line in ${\bf R}^2$ is a subspace if and only if it contains $0$. Suppose $V$ is a vectors space, what is a ''line in a vector space''?
  14 KB (2,471 words) - 21:48, 5 September 2011
• Calculus exercises: part I
  *The graph of a function $f$ is given below. Find an equation of the line secant to the graph at $(0,-1)$. *The secant line of the sign function are shown below. What do they tell you about the diffe
  49 KB (8,436 words) - 17:14, 8 March 2018
• Several variables
  ...he curve isn't the graph of any function of one variable as the ''Vertical Line Test'' is violated. $\square$ ...f change'' (also known as the difference quotient, the slope of the secant line, etc.):
  76 KB (13,017 words) - 20:26, 23 February 2019
• Derivative as a limit
  ''Derivative'' is the [[slope]] of the [[tangent line]]. But what ''is'' the tangent line? (Silly answer: Line the slope of which is equal to the derivative).
  5 KB (857 words) - 13:57, 25 May 2011
• 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
• 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
• 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

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