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• Topology Illustrated -- Index
  *[[line integral|line integral]] *[[line with two origins|line with two origins]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Vector calculus: midterm
  ##There is only one natural parametrization of a straight line. ...ic formula for the 3D-line through the point $(2,3,4)$ and parallel to the line through the points $(1,1,1)$ and $(-1,-2,-3)$.
  4 KB (674 words) - 02:48, 22 August 2011
• Limits: transition from discrete to continuous
  Suppose a real number $x$ is given. We construct a line segment of length $1$ on the plane. Then *$\cos x$ is the projection of the segment on the horizontal line,
  51 KB (9,271 words) - 20:02, 8 September 2016
• Physics
  ...e above formula still applies but, as we add them together, we produce a ''line integral'': ...varphi =fdx+gdy$ we construct a $0$-form $\psi$ with $d\psi =\varphi$ as a line integral. We fix a point $a \in {\bf R}^n$ and define $\psi$ as a function
  4 KB (778 words) - 16:47, 16 July 2014
• Quotients of vector spaces
  Then each equivalence class is a line: ...which appear in a 1-1 correspondence with the points on the other diagonal line.
  6 KB (1,115 words) - 16:03, 27 August 2015
• Velocity
  [[Image:tangent line examples.jpg|center]] ...[[tangent line]] to the circle at any point: the [[slope]] of the tangent line is equal to the value of the [[derivative]] of $f$ at the point.
  4 KB (662 words) - 15:17, 13 November 2012
• Internal structure of a vector space: part 1
  '''Answer:''' It's a line. Prove ${\rm span \hspace{3pt}} S = L$, the line diagonal through $0$.
  10 KB (1,614 words) - 17:13, 22 May 2012
• Homology groups of graphs
  Then each equivalence class is a line: ...appear to be in a 1-1 correspondence with the points of the other diagonal line $y=-x$.
  28 KB (4,685 words) - 17:25, 28 November 2015
• Cubical calculus
  ...he simplest setting, we deal with the intervals in the complex of the real line ${\mathbb R}$. Then the cochain assigns a number to each interval to indica One should recognize the second line as a line integral:
  25 KB (4,238 words) - 02:30, 6 April 2016
• Calculus 3: final
  8. Evaluate the line integral $\int_{C}x^{2}y^{3}dx-y\sqrt{x}dy$, where $C$ is parametrized by 9. (a) Explain what it means for a line integral $\int_{C}\mathbf{F}\cdot d\mathbf{r}$ to be independent of path. (
  4 KB (652 words) - 15:22, 9 March 2014
• Calculus I -- Fall 2017
  ...line segment (the path that lies on the hill) will be labeled as A and the line that lies on flat ground will be labeled as B. As for the x variable that **Number systems. Distance formula. Slope of a line. Standard equations of lines.
  13 KB (2,075 words) - 13:35, 27 November 2017
• Fantasy math
  The bottom line: the numerical/computational aspect should be built in! ...s. [[Vectors]]. The [[dot product]]. The [[cross product]]. Equations of [[line|lines]] and [[plane]]s. [[Vector functions]] and space curves. Derivatives
  8 KB (1,196 words) - 13:02, 24 August 2015
• The gradient
  ...the graph of a function of two variables and the flow seems to follow the line fastest descent; maybe our vector field is the gradient of this function? W ...h ''linear functions''. In other words, what if we travel along a straight line on a flat, not necessarily horizontal, surface (maybe a roof)? After this s
  74 KB (13,039 words) - 14:05, 24 November 2018
• Geometry of Euclidean space
  ...all vectors perpendicular to $x$? Let's call this set $S$. What is $S$? A line: ...ll vectors perpendicular to hyperplane $S$, then $Q = {\rm span}\{v \}$, a line through $0$, a $1$-dimensional subspace.</center>
  21 KB (3,396 words) - 20:31, 10 August 2011
• The integral
  \text{the line touching the curve at a point }&\text{ the area enclosed by the curve }\ \ ...continuous. We know that the area of a trapezoid is the length of the mid-line times the height. Then we have:
  66 KB (11,473 words) - 21:36, 19 January 2019
• Closedness and exactness of 1-forms
  ...varphi =fdx+gdy$ we construct a $0$-form $\psi$ with $d\psi =\varphi$ as a line integral. We fix a point $a \in {\bf R}^n$ and define $\psi$ as a function [[image:line integral for PL.png|center]]
  8 KB (1,421 words) - 13:41, 10 April 2013
• Vector calculus: exercises
  Find a tangent line to the curve parameterized by $f$ at the point $t=2$. ...Therefore, it suffices to simply use $f'(2)$ as a direction vector for the line. Further
  16 KB (2,457 words) - 02:17, 22 August 2011
• Continuous functions
  '''Exercise.''' To what is the Mobius band with the center line cut out homeomorphic? [[Image:point-point line.png|center]]
  42 KB (7,138 words) - 19:08, 28 November 2015
• Vector calculus: review
  #In an effort to find the line in which the planes $ 2x -y- z=2 $ and $-4x+2y+2z=1$ intersect, a student #Parametrically describe the line segment with endpoints $(-1,-1,-1)$ and $(1,1,1).$
  7 KB (1,394 words) - 02:36, 22 August 2011
• Derivative
  [[Image:tangent line examples.jpg|right]] ...circle]]. Then we [[differentiation|differentiate]] and find the [[tangent line]] to the circle at any point:
  4 KB (659 words) - 01:47, 30 August 2010

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