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• Operations on functions
  '''Example (intercepts).''' For a function $F:{\bf R}\to {\bf R}$, its graph is the following set given presented via Suppose $y=F(x)$ is a numerical function. Then the $x$-''intercepts'' of $F$ are the elements of the intersection of
  142 KB (23,566 words) - 02:01, 23 February 2019
• Functions
  [[image:boys and balls -- relation and function.png| center]] [[image:boys and balls -- function.png| center]]
  151 KB (25,679 words) - 17:09, 20 February 2019
• Precalculus
  *1. finding the distance between two points, and For example, suppose $P$ is a ''location'' on the line. We then find the distance from the origin -- positive in the positive direction and negative in the n
  100 KB (16,148 words) - 20:04, 18 January 2017
• Calculus I, the discrete version
  *a node function $f: 0\mapsto 2,\ 1\mapsto 4,\ 2\mapsto 3,\ ...$; and *an edge function $s: [0,1]\mapsto 3,\ [1,2]\mapsto .5,\ [2,3]\mapsto 1,\ ...$.
  64 KB (11,521 words) - 19:48, 22 June 2017
• Classes of functions
  Now, what if ''all'' boys prefer basketball? Then the “preference function” $F$ cannot be simpler: all of its values are equal and all arrows point The table of this function $F$ is also very simple: all crosses are in the same column; and the graph
  143 KB (24,052 words) - 13:11, 23 February 2019
• Differentiation
  ...What this means is that this procedure is a special kind of function, a ''function of functions'': ...hat this means is that this process is a special kind of function too, a ''function of functions'':
  82 KB (14,116 words) - 19:50, 6 December 2018
• Functions of several variables
  ...ons. On the other hand, we can see that the surface that is the graph of a function of two variables produces -- through cutting by vertical planes -- ''infini We represent a function diagrammatically as a ''black box'' that processes the input and produces t
  97 KB (17,654 words) - 13:59, 24 November 2018
• Limits and continuity
  One of the most crucial properties of a function is the integrity of its graph: ''is there a break or a cut?'' For example, If there is a jump in the graph of the function, it can't represent motion!
  107 KB (18,743 words) - 17:00, 10 February 2019
• Functions in higher dimensions
  ...early calculus (Chapters 7 -13) we deal with only numbers, the graph of a function of one variable lies in the $xy$-plane, a space of dimension $2$. [[image:function of two variables -- heat map.png| center]]
  113 KB (19,680 words) - 00:08, 23 February 2019
• Applications of integral calculus
  ...preadsheet, $\sum_i f(c_i)\cdot.1$, and them subtract the data for the new function, $\sum_i g(c_i)\cdot.1$. Furthermore, we have ...he following. We ''recognize'' this expression as the Riemann sum of a new function, $f-g$:
  103 KB (18,460 words) - 01:01, 13 February 2019
• Calculus exercises: part I
  It's just a limit. But we recognize that this is the derivative of some function. We compare the expression to the formula in the definition: The function is computed in two steps. Indeed, if
  49 KB (8,436 words) - 17:14, 8 March 2018
• Differential calculus of parametric curves
  A parametric curve is such a function: ...the latter vector, $OX$. In either case, this is just a combination of two function of the same independent variable.
  130 KB (22,842 words) - 13:52, 24 November 2018
• The derivative
  We approached the problem by plotting the location as a function of time: [[image:location as a function of time.png| center]]
  75 KB (13,000 words) - 15:12, 7 December 2018
• Differential calculus
  *maximize the function $A(W)=-W^2+50W$. [[image:cattle -- function 2.png| center]]
  84 KB (14,321 words) - 00:49, 7 December 2018
• Several variables
  ...formulas can now be solved in order to be able to model the location as a function of time. The result is these recursive formulas for the ''Riemann sums'': ...00$ and $0$ respectively. Below, the velocity is computed as a Riemann sum function of the previous column, with the same formula:
  76 KB (13,017 words) - 20:26, 23 February 2019
• Vector and complex variables
  ...real-valued functions of two variables. Consider $u=f(x,y)=2x-3y$, such a function: Consider another such function: $v=g(x,y)=x+5y$ is also a real-valued function of two variables:
  113 KB (18,750 words) - 02:33, 10 December 2018
• The integral
  ...nfirm the formula with nothing but a spreadsheet. We plot the graph of the function: ...e development of algebra, the Cartesian coordinate system, and the idea of function (Chapters 2, 3, and 4).
  66 KB (11,473 words) - 21:36, 19 January 2019
• Precalculus exercises
  ...)=x^2+3x-10$. Find the $x$- and $y$-intercepts and sketch the graph of the function. *What is the distance from the center of the circle $(x-1)^2+(y+3)^2=5$ to the origin?
  17 KB (2,933 words) - 19:37, 30 July 2018
• Freshman's introduction to discrete calculus
  *a node function $f: 0\mapsto 2,\ 1\mapsto 4,\ 2\mapsto 3, ...$; and *an edge function $s: [0,1]\mapsto 3,\ [1,2]\mapsto .5,\ [2,3]\mapsto 1, ...$.
  42 KB (7,443 words) - 14:18, 1 August 2016
• Vector fields
  *$r$ is the distance between the centers of the masses. That's the vector form of the law! We plot the magnitude of the force as a function of two variables:
  91 KB (16,253 words) - 04:52, 9 January 2019
• 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
• Vector integrals
  Given motion with the position function $F : {\bf R} {\rightarrow} {\bf R}^n$ during a time interval $[ a, b ]$, we [[Image:lengths - displacement and distance traveled.jpg|right]]
  15 KB (2,545 words) - 19:47, 20 August 2011
• Introduction to discrete calculus
  ...es of $1$-chains are $0$-chains as well. Then, boundaries are found by the function defined above: ...e think initially of a <!--\index{cochain}--> $k$-cochain as a real-valued function defined on $k$-cells of ${\mathbb R}$.
  40 KB (6,983 words) - 19:24, 23 July 2016
• Treat calculus discretely!
  Let's plot our location as a function of time: [[image:location as a function of time.png| center]]
  8 KB (1,196 words) - 12:02, 4 July 2018
• Homeomorphism
  Homeomorphisms are [[continuous functions]]<!--\index{ continuous function}--> that preserve topological properties. That's why we will define a class of maps so that both the function
  13 KB (2,168 words) - 13:09, 7 August 2014
• Metric tensor
  ..., or deforming the $x$- or the $y$ axes won't change the monotonicity of a function but it will change its concavity. '''Proposition.''' Given a differentiable function $f:{\bf R}\to {\bf R}$,
  42 KB (7,131 words) - 17:31, 30 November 2015
• Maps of polyhedra
  ...f such as approximation is a ''sequence'' of polynomials converging to the function. This time the goal is ...nts will be allowed. Instead, we start with the simple idea of using “cell distance” as one and only “measurement” of closedness.
  51 KB (9,162 words) - 15:33, 1 December 2015
• Inner product spaces: part 1
  Consider the [[distance formula]] in ${\bf R}^2$. Then, the distance from $d=(a,b)$ to $0$ is $\sqrt{a^2+b^2}$.
  14 KB (2,404 words) - 15:04, 13 October 2011
• Binary watershed
  ...geJ.jpg|(1) the original image of particles that touch each other, (2) the distance of each pixels to the nearest white pixel is illustrated with its gray leve ...est white pixel. This is called the [[distance function]]. It’s a [[scalar function]] of two variables.</p>
  5 KB (747 words) - 22:05, 16 May 2010
• Sequences and their limits
  Even though every function $y=f(x)$ with an appropriate domain creates a sequence, $a_n=f(n)$, the con A function defined on a ray in the set of integers, $\{p,p+1,...\}$, is called an ''in
  64 KB (10,809 words) - 02:11, 23 February 2019
• Convergence of the discrete to the continuous
  The diagram commutes. Indeed, given a function $f:{\bf R}\to {\bf R}$, we can proceed in two ways: *right then down: we acquire a $0$-form $g$ by sampling function $f$, and then we acquire $dg$ by taking the differences of the values of $g
  21 KB (3,664 words) - 02:02, 18 July 2018
• Geometry
  ..., or deforming the $x$- or the $y$ axes won't change the monotonicity of a function but it will change its concavity. '''Proposition.''' Given a differentiable function $f:{\bf R}\to {\bf R}$,
  41 KB (6,928 words) - 17:31, 26 October 2015
• Preview of calculus: part 2
  The [[absolute value]] function Function \( y=f(x) \) is ''increasing on interval'' \( (a, b) \) if for any given \(
  19 KB (2,850 words) - 15:04, 19 March 2011
• Pattern recognition in computer vision
  ...lem. Suppose the distance between (1,0,…,0) and (0,1,0,…,0) is d. Then the distance between (1,0,…,0) and (0,0,…,0,1) is also d. Here (1,0,…,0) and (0,1, ...A and B are in the same cluster, then so is C. So adjacency of pixels and distance between them is lost in this representation!</p>
  9 KB (1,526 words) - 17:54, 1 July 2011
• Limits: part 1
  '''Solution:''' We'd approach the problem by computing the distance covered during the last: $$ \text{average speed} = \dfrac{\text{distance}}{\text{time}}. $$
  10 KB (1,609 words) - 16:13, 2 May 2011
• Set-valued maps
  It can also be thought of as a function to the power set of $Y$: ...continuous function $f:X\to Y$ doesn't, of course, have to be a continuous function.
  24 KB (4,382 words) - 15:52, 30 November 2015
• Integral: introduction
  and the numerator is the difference of the values of the function $f(b) - f(a)$. $$\text{Distance covered } = 60 + 65 + 50 \qquad \text{(addition!)}. $$
  3 KB (466 words) - 17:26, 20 July 2011
• Reversing differentiation: antiderivatives
  ...es" the effect of differentiation. In that sense it's similar to [[inverse function]]. *Given position (as a function of time),
  8 KB (1,349 words) - 22:16, 17 July 2011
• Geometry of Euclidean space
  Based on the formula for the norm, we have the ''distance formula'' for ${\bf R}^n$ (Image) #the projection gives you the shortest distance to $L$.
  21 KB (3,396 words) - 20:31, 10 August 2011
• Tangent bundles
  $$\text{ work } = \text{ force }\cdot \text{ distance}.$$ ...r negative and we should speak of the ''displacement'' $D$ rather than the distance. We then amend the formula:
  16 KB (2,753 words) - 13:55, 16 March 2016
• Preview of calculus: part 1
  ...) as straight lines are defined by two points. Instead, we keep making the distance between \(A\) and \(B\) smaller. ...nted by the data in the table. These data in the table represents the same function above but, as we can see, there are gaps in the data. We can't tell, for ex
  10 KB (1,532 words) - 00:07, 2 May 2011
• Forms
  <center>Work = force $\cdot$ distance.</center> ...e positive or negative and we should speak of ''displacement'' rather than distance. We then amend the formula as:
  13 KB (2,459 words) - 03:27, 25 June 2015
• Robustness of topology of digital images and point clouds by Saveliev
  ...sure of robustness of the homology classes of the lower level sets of this function \ELZ, \Carlsson, \CZ09, \CZ. First, a [[gray scale image]] is a real-valued function $f$ defined on a rectangle. Given a threshold $r$, the lower level set $f^{
  27 KB (4,547 words) - 04:08, 6 November 2012
• Products
  However, this isn't the definition of continuity of a function of two variables (that would make it dependent on the choice of the Cartesi ...''' Prove that the metric $d$ of a metric space $(X,d)$ is continuous as a function $d:X\times X\to {\bf R}$ on the product space.
  44 KB (7,951 words) - 02:21, 30 November 2015
• Introductory algebraic topology: review exercises
  *[[Is a restriction of a continuous function always continuous? ]] *[[Is the inverse of a continuous function always continuous? ]]
  9 KB (1,553 words) - 20:10, 23 October 2012
• Metric complexes
  ...efinition.''' An ''inner product''<!--\index{inner product}--> on $V$ is a function that associates a number to each pair of vectors in $V$: ...on.''' Given a vector space $V$, a ''norm''<!--\index{norm}--> on $V$ is a function
  35 KB (5,871 words) - 22:43, 7 April 2016
• Integral: properties
  # Constant function rule: ...ng the 1st hour } + \text{ distance covered during the 2nd hour } = \text{ distance during 2 hours}$$
  3 KB (456 words) - 23:26, 20 July 2011
• Calculus as a part of topology
  The early calculus is about the derivative, i.e., the rate of change of a function. This doesn't seem like a part of Topology, Algebra, and Geometry. However, *For every two points, what is the distance between them?
  13 KB (2,233 words) - 14:41, 20 February 2015
• Integral: definition
  $$ \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
• Compact spaces
  ...\index{path-connectedness}--> (under a continuous map<!--\index{continuous function}-->) is a path-connected. ...losed or not bounded. We will seek a single condition on the domain of the function that would guarantee that the theorem holds. As the counterexamples show, i
  19 KB (3,207 words) - 13:06, 29 November 2015
• Calculus I -- Fall 2017 -- final
  $\bullet$ '''1.''' Describe the behavior of the function plotted below without referring to the picture: [[image:Rational function with several asymptotes.png| center]]
  2 KB (262 words) - 19:15, 12 December 2017
• Elementary PDEs
  *inversely, to the distance between the centers of mass of the rooms (dually: the length of the pipe). ...e.''' Find the speed of propagation of the material in a uniform grid as a function of the length of the cell.
  16 KB (2,843 words) - 21:41, 23 March 2016
• Calculus I -- Fall 2017
  ...lattens out is 5 miles north from the origin. This means that the minimum distance of the hillside that the hiker will be climbing is 7.07 miles if traveling **Number systems. Distance formula. Slope of a line. Standard equations of lines.
  13 KB (2,075 words) - 13:35, 27 November 2017
• PDEs
  *inversely, to the distance between the centers of mass of the rooms (dually: the length of the pipe). ...nsider two issues. First, let's recall that when studying ODEs we used the function $q:C_1({\mathbb R})\to C_0({\mathbb R})$ given by
  44 KB (7,469 words) - 18:12, 30 November 2015
• Limits: part 3
  How? We have the average speed as a function of time. # the [[distance formula|distance]] from $x$ to 1 is less than $\delta$, or
  17 KB (2,737 words) - 16:05, 2 May 2011
• Simplicial complexes
  ...''proximity'' of the elements of $P$ and this proximity can't rely on any distance. Instead we define the topology of $\Delta (P)$ in terms of the order relat Sometimes these preferences are captured by a single function.
  30 KB (5,021 words) - 13:42, 1 December 2015
• Limits at infinity: part 1
  Consider what happens when we take the inverse of a function. ...limits_{x \to a}$, a number, is about the local/short term behavior of the function.\
  5 KB (819 words) - 13:54, 25 May 2011
• Diffusion
  #and, inversely, to the distance between the centers of mass of the rooms (the length of the pipe). '''Exercise.''' Find the speed of propagation in a uniform grid as a function of the length of the cells.
  39 KB (6,850 words) - 15:29, 17 July 2015
• Discrete Calculus: Applied Analysis on Graphs for Computational Science by Grady and Polimeni
  ...esult: the line integral over $1 \times 1$ square of the [[gradient]] of a function isn't zero ([[path independence]]). Score for [[discrete exterior calculus] ...globally. Why does the metric have to be Euclidean? For data the Euclidean distance is meaningless. In fact, why does the dataset have to be a [[metric space]]
  11 KB (1,663 words) - 16:03, 26 November 2012
• Gray scale watershed
  Suppose we have a function f(x,y) and a surface that is the graph of f. Next, we flood the valley and <p>In the standard settings when f(x,y) is the [[gray scale function]] of the image (in the example on the right f(x,y)=sin(x)sin(y)), what is c
  4 KB (645 words) - 04:10, 28 January 2010
• College Algebra -- Fall 2014 -- final exam
  $\bullet$ '''2.''' What is the distance from the center of the circle $(x-1)^2+(y+3)^2=5$ to the origin? $\bullet$ '''3.''' Plot the graph of the function $y=f(x)$, where $x$ is the income (in thousands of dollars) and $f(x)$ is t
  2 KB (410 words) - 03:09, 6 November 2018
• Physics
  where $d$ is the distance moved. This is how we solve the "exactness problem". Given a continuous function $f$, it is exact if it's the derivative of something:
  4 KB (778 words) - 16:47, 16 July 2014
• Topology
  grass/undergrowth/forest, hills/valleys, wet/dry, distance to the road/river/lake, etc. If the landowner only had a single criterion f ...value, the better the choice. These numbers form what's called a “utility function”:
  20 KB (3,407 words) - 21:46, 30 November 2015
• Fantasy math
  Sometimes there is a [[continuous function]] or process behind the numbers but often there isn't. The issues one has t What is commonly done is to go back to [[continuous function]]s via [[approximation]], [[interpolation]], [[curve fitting]], etc. This a
  8 KB (1,196 words) - 13:02, 24 August 2015
• Clustering
  ...A and B are in the same cluster, then so is C. So adjacency of pixels and distance between them is lost in this representation!</p> ...e squares become smaller. In the end we have a - possibly [[continuous]] – function (as the limit of this sequence of functions see [[Convergence]]). This is t
  3 KB (477 words) - 19:14, 28 August 2010
• Calculus I -- Fall 2016
  ...ling if the amount of light is inversely proportional to the square of the distance? **Number systems. Distance formula. Slope of a line. Standard equations of lines.
  11 KB (1,671 words) - 23:11, 13 December 2016
• Calculus I -- Spring 2017
  ...ling if the amount of light is inversely proportional to the square of the distance? -- ([http://users.marshall.edu/~saveliev/Teaching/Spring17/Projects/best_i **Number systems. Distance formula. Slope of a line. Standard equations of lines.
  12 KB (1,803 words) - 20:50, 1 May 2017
• Data made Euclidean
  ...proximity'' of the elements of $P$ and this proximity doesn't rely on the "distance" as it may be missing from the ordered set. Instead we define the topology ...For example, one may prefer: rain > snow > hail, and define the ''utility function'' $u$ by assigning:
  31 KB (5,219 words) - 15:07, 2 April 2016
• Homology groups of filtrations
  ...ame functions $f,g.$ Function $F(x,y)=y-x$ creates an analogue bottle-neck distance for the set of points $\{persistence\}\subset \mathbf{R} $ and its stabilit
  4 KB (621 words) - 13:27, 28 August 2015
• Dilation and erosion
  ...]] may be preferable (the n-th round turns all white pixels within n-pixel distance from the "seed", black.).
  3 KB (408 words) - 14:55, 13 March 2011
• College Algebra by Sullivan
  2.1 The Distance and Midpoint Formulas 3.2 The Graph of a Function
  3 KB (349 words) - 16:29, 8 August 2013
• Derivative reflects behavior of the function
  We consider some theory about how one can find out about the behavior of the function from its [[derivative]]. ...ime $x$. Then speed/[[velocity]] corresponds to the derivative $f'$ of the function.
  8 KB (1,470 words) - 00:39, 16 July 2011
• Calculus 1: exercises
  ...x)=x²+3x-10$. Find the $x$- and $y$-intercepts and sketch the graph of the function. *Sketch the graph of a function f that has the following property: f is increasing and concave down on $[-1
  3 KB (435 words) - 19:23, 13 June 2011
• Topology of proteins
  ...follows. Each atom is a point in space and a vertex in the complex. If the distance between two atoms is less that the sum of their van der Waals radii they sh ...overed as well the thousands of known proteins in order to determine their function with a high degree of confidence. The algorithms will also apply to inorgan
  2 KB (316 words) - 21:16, 2 October 2011
• College Algebra -- Fall 2013
  2.1 The Distance [and Midpoint] Formulas 3.2 The Graph of a Function
  6 KB (752 words) - 04:19, 13 December 2013
• College Algebra -- Fall 2014
  2.1 The Distance [and Midpoint] Formulas 3.2 The Graph of a Function
  6 KB (850 words) - 16:52, 29 November 2014
• Parametric surfaces
  This will be the [[domain]] of this function: <center>$( x, y, z ) \in S( 0, 1 )$ iff $x^2 + y^2 + z^2 = 1$ (distance to $0$ is $1$).</center>
  3 KB (391 words) - 21:12, 28 August 2011
• Stability Analysis
  ...rary time and space steps, but rewrite F as u and our variables within the function as subscripts, with i denoting x, j denoting y, and n denoting our time-ste ...xagonal-Grid, meanwhile, the space-steps should be the same size '''AS THE DISTANCE BETWEEN THE CENTERS OF TWO ADJACENT HEXAGONS'''! And, for the triangular g
  12 KB (2,051 words) - 03:51, 11 August 2012
• Metric
  ...X \times X \longrightarrow {\bf R}$ is called a ''metric'' (or a "distance function") if, for every $x,y,z \in X$,
  531 bytes (104 words) - 05:14, 18 February 2011
• Diffusion equation
  *inversely, to the distance between the centers of mass of the rooms (dually: the length of the pipe). ...nsider two issues. First, let's recall that when studying ODEs we used the function $q:C_1({\mathbb R})\to C_0({\mathbb R})$ given by
  35 KB (5,917 words) - 12:51, 30 June 2016
• Calculus I -- Fall 2018
  **Number systems. Distance formula. Slope of a line. Standard equations of lines. **The limit of a function at a point. One-sided limits. Continuity and the intermediate value theorem
  8 KB (1,184 words) - 17:55, 29 October 2018
• Image Sequences
  ...is (roughly) the minimal diameter of in the feature, D, minus the largest distance between any point and two of its nearest neighbors, B. Therefore, incidenta ...as well as any combinations of them. He can also create his own Evaluation function by choosing his own integrands, or his own settings.
  19 KB (2,899 words) - 13:33, 29 May 2009
• Inner product spaces: part 2
  This is the ''distance between functions''. '''Analysis:''' The set of [[differential function]]s $C^1({\bf R})$ and we want to find the functions closest to $\sin$... cl
  10 KB (1,688 words) - 17:59, 13 October 2011
• Discrete Calculus -- Preface
  *displacement and distance, ...''. In calculus, we study the rates of change of functions. For a discrete function, this is a simple ratio. That's how we define the derivatives. Their values
  2 KB (345 words) - 03:06, 27 August 2016
• Peter Saveliev's Academic Portfolio
  Sometimes there is a [[continuous function]] or process behind the numbers but often there isn't. The issues one has t ...n ways to generate 3D reference points using stereo vision to estimate the distance of obstacles, such as ocean vehicles and coastlines. The resulting system w
  25 KB (3,536 words) - 14:28, 17 January 2017
• Wave equation
  Let $u(t,x)$ be the function that measures the displacement from the equilibrium of the object associate ...possibly variable) distances $\Delta x, \Delta y$ to its neighbors and the distance between the centers of the springs has length $\Delta x^\star, \Delta y^\st
  10 KB (1,775 words) - 02:40, 9 April 2016
• Measurement statistics of fibers
  ...figuring out how [[Pixcavator]] can help them to automatically carry out a function that they currently do manually. They were looking for a method to automati ...of the one inch part of the ruler: (193,235) and (196,44). This gives the distance between them:</p>
  3 KB (437 words) - 16:19, 4 March 2011