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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

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