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• Riemann integral
  *let $f: n-dim$ box $→ ℝ$ be scalar function, then and call $f$ an [[integrable function]] on $[ a, b ]$.
  2 KB (361 words) - 16:47, 30 September 2013
• Integral: definition
  $$ \text{Upper half of the circle } = \text{ the graph of this function }$$ We will approximate by "sampling" our function at several values of $x$, $n$ of them.
  9 KB (1,406 words) - 19:50, 20 July 2011
• Images as functions of two variables
  .... The union of these squares gives us the [[domain]] of the function. This function has only two possible values. ...2⁸ levels of gray. These numbers together form the ''gray scale function'' of the image. An example is on the right.
  3 KB (498 words) - 03:05, 29 August 2010
• Real analysis: final 1
  ...ble function $f:\mathbf{R}^{N}\rightarrow\mathbf{R.}$ Give an example of a function $f:\mathbf{R}^{2}\rightarrow\mathbf{R}$ such that both partial derivatives #Give example of such a function $f:\mathbf{R}^{2}\rightarrow\mathbf{R}$ that $f$ is not continuous at $(0,0
  3 KB (562 words) - 20:29, 13 June 2011
• Calculus as a part of topology
  The early calculus is about the derivative, i.e., the rate of change of a function. This doesn't seem like a part of Topology, Algebra, and Geometry. However, We will approximate by "sampling" our function at several values of $x$, $n$ of them.
  13 KB (2,233 words) - 14:41, 20 February 2015
• The algebra of oriented cells
  ...or any given integrable function $f:[A,B]\to {\bf R}$, we can define a new function: Then, according to the above identities, this function is ''linear''<!--\index{linearity}-->! Indeed, we've shown:
  36 KB (6,395 words) - 14:09, 1 December 2015
• More on vector spaces
  ==Function spaces== *$f$ represents the function as a whole, and
  14 KB (2,471 words) - 21:48, 5 September 2011
• Integral theorems of vector calculus
  ...ion of two variables]]. This function is constant on each pixel, so it's [[integrable]]. Then be a function with [[continuous]] [[derivative]], and $R$ a simple region. Then
  16 KB (2,752 words) - 14:18, 28 December 2012
• Discrete parametric curves
  ...omain, the $t$-axis, with the same nodes... Then, the $2$-dimensional node function (a curve) is Given motion with the position function $F : {\bf R} \to {\bf R}^n$ during a time interval $[ a, b ]$, we have two
  32 KB (5,426 words) - 21:57, 5 August 2016
• Independence of path
  It is sufficient for the force to have a [[potential function]]: '''Theorem.''' If $F$ has a potential function, then it is conservative:
  5 KB (883 words) - 20:41, 20 August 2011
• Real analysis: test 2
  #Give example of such a function $f:\mathbf{R}^{2}\rightarrow\mathbf{R}$ that $f$ is not continuous at $(0,0 #Describe Newton's method. Give an example of a function for which the method does not apply.
  2 KB (275 words) - 20:30, 13 June 2011
• Fourier coefficients
  ...= e^{inx}: n \in Z\}$ is an [[orthonormal basis]] for the space of square-integrable functions of $[−π, π]$. This space is an [[inner product space]]: ...can be expressed in terms of the Fourier coefficients $\hat{f}(n)$ of the function $f$:
  1 KB (188 words) - 23:36, 21 May 2013
• Volume as an integral
  and call f an [[integrable function]] on [ a, b ].
  3 KB (513 words) - 02:51, 17 August 2010
• Fundamental Theorem of Calculus
  For an [[integrable]] function $f$,
  605 bytes (107 words) - 20:19, 28 August 2011
• Area integral
  and call $f$ an [[integrable function]] on $[ a, b ]$.
  3 KB (414 words) - 03:45, 22 August 2011

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