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# Difference between revisions of "Discrete calculus article"

(Created page with "'''Discrete calculus''' or "the calculus of discrete functions", is the mathematical study of ''incremental'' change, in the same way that geometry is the...") |
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− | '''Discrete calculus''' or "the calculus of discrete functions", is the [[mathematics|mathematical]] study of ''incremental'' change, in the same way that [[geometry]] is the study of shape and [[algebra]] is the study of generalizations of [[arithmetic operations]]. The word ''calculus'' | + | '''Discrete calculus''' or "the calculus of discrete functions", is the [[mathematics|mathematical]] study of ''incremental'' change, in the same way that [[geometry]] is the study of shape and [[algebra]] is the study of generalizations of [[arithmetic operations]]. The word ''calculus'' is a [[Latin]] word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, '''[[calculus]]''', originally called '''infinitesimal calculus''' or "the calculus of [[infinitesimal]]s", is the study of ''continuous'' change. |

It has two major branches, [[differential calculus]] and [[integral calculus]]. Differential calculus concerns incremental rates of change and the slopes of discrete curves. Integral calculus concerns accumulation of quantities and the areas under and between such curves. These two branches are related to each other by the [[fundamental theorem of discrete calculus]]. | It has two major branches, [[differential calculus]] and [[integral calculus]]. Differential calculus concerns incremental rates of change and the slopes of discrete curves. Integral calculus concerns accumulation of quantities and the areas under and between such curves. These two branches are related to each other by the [[fundamental theorem of discrete calculus]]. | ||

+ | |||

+ | The concepts of change start in their discrete form. Then by making the increment smaller and smaller, we find the ''limit'': | ||

+ | $$\newcommand{\ra}[1]{\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!} | ||

+ | \begin{array}{ccccc} | ||

+ | \begin{array}{|cc|}\hline\text{ discrete }\\ \text{ calculus }\\ \hline\end{array}& \ra{\quad\Delta x\to 0\quad} &\begin{array}{|cc|}\hline\text{ infinitesimal }\\ \text{ calculus }\\ \hline\end{array} | ||

+ | \end{array}$$ |

## Revision as of 15:57, 28 August 2019

**Discrete calculus** or "the calculus of discrete functions", is the mathematical study of *incremental* change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word *calculus* is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, **calculus**, originally called **infinitesimal calculus** or "the calculus of infinitesimals", is the study of *continuous* change.

It has two major branches, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of discrete curves. Integral calculus concerns accumulation of quantities and the areas under and between such curves. These two branches are related to each other by the fundamental theorem of discrete calculus.

The concepts of change start in their discrete form. Then by making the increment smaller and smaller, we find the *limit*:
$$\newcommand{\ra}[1]{\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!}
\begin{array}{ccccc}
\begin{array}{|cc|}\hline\text{ discrete }\\ \text{ calculus }\\ \hline\end{array}& \ra{\quad\Delta x\to 0\quad} &\begin{array}{|cc|}\hline\text{ infinitesimal }\\ \text{ calculus }\\ \hline\end{array}
\end{array}$$