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• 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
• Differentials
  ...\frac{dy}{dx}\bigg| _a$ = the derivative at $a$ = the slope of the tangent line through $(a,f(a))$ = $\frac{rise}{run}$ </center> The slope of the [[secant line]] is $m = \frac{\Delta y}{\Delta x}$, or
  1 KB (243 words) - 18:13, 22 August 2015
• Integral theorems of vector calculus
  ...now. Then, in a similar way, an [[area integral]] can be expressed as a [[line integral]], somehow: ...} FTC) \hspace{3pt} (interpret \hspace{3pt} as \hspace{3pt} a \hspace{3pt} line \hspace{3pt} integral)} \\
  16 KB (2,752 words) - 14:18, 28 December 2012
• Affine approximation
  As the picture shows, a curve is approximated by a straight line while a [[surface]] by a plane. ...in on the graph of a [[differentiable function]], it looks like a straight line.
  7 KB (1,162 words) - 03:25, 22 August 2011
• Limits: part 1
  **on the line through $A$ that is perpendicular to the diagonal, Estimate the [[tangent line]] of a function given [[numerical representation of functions|numerically]]
  10 KB (1,609 words) - 16:13, 2 May 2011
• Applications of derivative: optimization
  Find a point on the line $y=4x + 7$ closest to the origin. [[Image:Origin.png|none|Closest distance to origin for line $y = 4x + 7$.]]
  6 KB (891 words) - 02:15, 17 July 2011
• Linear approximations
  We know that the [[tangent line]] "approximates" the [[graphs of functions|graph]] of $y=f(x)$ around $x=a$ ...case, when you zoom in on the point, the tangent line will (but any other line won't) merge with the graph. This is the geometric meaning of ''best approx
  2 KB (384 words) - 15:44, 2 May 2011
• Applied Calculus -- Spring 2015
  **0.1 The Real Number Line and Order **0.2 Absolute Value and Distance on the Real Number Line
  9 KB (1,141 words) - 16:08, 26 April 2015
• Manifolds model a curved universe
  ...ment 1: with light from a star passing the sun and deviating from straight line. by using the graph of $f$. But for $dy$, we use the tangent line instead:
  10 KB (1,588 words) - 17:11, 27 August 2015
• More about manifolds
  Here $f^{-1}(A)$ is all these points, a whole line! Why? Because: there is no change of $F$ in this direction. ...tersection of these planes is "[[transversal]]", so that it's a line. This line approximates the intersection of the graph with the plane. It turns out to
  9 KB (1,542 words) - 19:58, 21 January 2014
• 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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