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• Integration
  Suppose a function $f$ is defined on an open interval $I$. Then a function $F$ defined on $I$ that satisfies $F' = f(x)$ for all $x$ is called an ''an ...eorem of Calculus).''' (I) Given a continuous function $f$ on $[a,b]$, the function defined by
  69 KB (11,727 words) - 03:34, 30 January 2019
• Calculus of chain maps
  First, $f$ has to be a function that takes nodes to nodes: ...h first and then attach edges to them. Therefore, we require from the edge function $f$ the following:
  41 KB (7,344 words) - 12:52, 25 July 2016
• Series
  ...t is called its best linear approximation and its happens to be the linear function the graph of which is the tangent line at the point. The replacement is jus However, there is a more basic approximation: a constant function, $y=C(x)$.
  113 KB (19,100 words) - 23:07, 3 January 2019
• Continuous functions
  First we, informally, discussed continuity of a function as a transformation that does not tear things apart and interpreted this id <!--200-->[[Image:continuous function.png|center]]
  42 KB (7,138 words) - 19:08, 28 November 2015
• Discrete calculus article
  ...ving the squaring function turns out to be something close to the doubling function. ...xteen, and so on—and uses this information to output another function, the function $g(x)=2x+h$, as will turn out. It is defined at the middle points of the ab
  27 KB (4,329 words) - 16:02, 1 September 2019
• Applications of differential calculus
  Given a function $y=f(x)$, find such a $d$ that $f(d)=0$. We have a function $f$ is defined and is continuous on interval $[a,b]$ with $f(a)<0,\ f(b)>0$
  59 KB (10,063 words) - 04:59, 21 February 2019
• Differential equations
  ...re, the ''difference'' of a function $y$ defined at the primary nodes is a function defined at the secondary nodes of the partition: We can also think of this sequence as a function defined at the nodes of the partition:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Functions of several variables: derivatives and integrals
  ==The derivative of a function of several variables== The linear approximations of a function $z=f(X)$ at $X=A$ in ${\bf R}^n$ are linear functions with $n$ slopes in th
  42 KB (6,904 words) - 15:15, 30 October 2017
• Applications of ODEs
  *the unit vector in this direction (dividing by the distance between them); ...the mass is equal to $1$. Then the ''kinetic energy'' is known to be this function of time:
  50 KB (8,692 words) - 14:29, 24 November 2018
• Partial differential equations
  ...id this “overshoot”, the increment of the heat shouldn't be more that half-distance to the heat of the other room. This is the result of our simulation is the collection of graphs of the function $u(t,\cdot)$ of one variable for each $t$ (the graph of $u$ is of course a
  53 KB (9,682 words) - 23:19, 18 November 2018
• Topological spaces
  There are no measurements in topology. Does the distance between a point and a set make any sense? Let's just try to decide if the distance is $0$ or not.
  27 KB (4,693 words) - 02:35, 20 June 2019
• Discrete forms and cochains
  ...$ is often thought of as a function the input of which is any integrable ''function'' $f$ while the output is a real number. This idea is revealed by the usual ...the limit of the Riemann sums of $f$. The student then discovers that this function is ''linear'':
  34 KB (5,619 words) - 16:00, 30 November 2015
• Integrals of functions of several variables
  *the height of the bar in this rectangle equal to the value of the function and with the ones outside the domain replaced with $0$s, and Suppose a function $y = f(X)=f(x,y)$ defined at the tertiary nodes of the partition of the rec
  73 KB (13,324 words) - 14:06, 24 November 2018
• Calculus of sequences
  ...{ speed }= \text{ distance } / \text{ time }\quad \text{ and }\quad \text{ distance }=\text{ speed }\times \text{ time }. \quad \\ \hline\end{array}$$ The formula is solved for the distance or for the speed depending on that is known and what is unknown.
  113 KB (18,425 words) - 13:42, 8 February 2019
• Discrete forms
  '''Definition.''' A ''cubical'' $k$-''form'' is a function defined on $k$-cells. To emphasize the nature of a form as a function, we can use arrows:
  35 KB (6,055 words) - 13:23, 24 August 2015
• Relative topology
  ...distance formula, the Euclidean metric<!--\index{Euclidean metric}-->. The distance between $(x,y)$ and $(a,b)$ is '''Theorem.''' Suppose $f : X \to Y$ is continuous<!--\index{continuous function}-->. If $X$ is path-connected<!--\index{path-connectedness}--> the so is $f
  34 KB (6,089 words) - 03:50, 25 November 2015
• Calculus on cubical complexes
  ...''' A ''cubical''<!--\index{cubical form}--> $k$-''form'' is a real-valued function defined on $k$-cells of ${\mathbb R}^n$. To emphasize the nature of a form as a function, we can use arrows:
  36 KB (6,218 words) - 16:26, 30 November 2015
• Applications of derivative: optimization
  Substitute to create a function of a ''single'' variable: Eliminate the extra variables to create a function of single variable to be maximized or minimized.
  6 KB (891 words) - 02:15, 17 July 2011
• Discrete parametric curves
  Consider the distance formula in ${\bf R}^2$. Then, the distance from $d=(a,b)$ to $0$ is $\sqrt{a^2+b^2}$.
  32 KB (5,426 words) - 21:57, 5 August 2016
• Topology Illustrated -- Index
  *[[constant function|constant function]] *[[continuous function|continuous function]]
  16 KB (1,773 words) - 00:41, 17 February 2016

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