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Discrete Calculus Brian Hamrick 1 Introduction How many times have you wanted to know a good reason that Xn i=1 i = n(n+1) 2. Sure, it’s true by induction, but how in the world did we get this formula? Or Xn i=1 i2 = n(n+1)(2n+1) 6? Well, there are several ways to arrive at these conclusions, but Discrete Calculus is one of the most beautiful.

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. Building on a large body of original research at Wolfram Research, the Wolfram Language for the first time delivers a comprehensive system for discrete calculus.

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 ...

The field of discrete calculus, also known as "discrete exterior calculus", focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space.

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.

discrete) analogue of infinite calculus so the finite sum X2 x=1 x2 is no more difficult to solve than the “infinite” sum Z 2 1 x2 dx. Besides finite calculus, another way to compute the value of Pn x=1 x 2 is to look it up in a book, or try and guess …

Here, we create a similar system for discrete functions. 2 The Discrete Derivative. We define the discrete derivative of a function f(n), denoted ∆nf(n) ...

Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and mathematical logic. Included within theoretical computer science is the study of algorithms and data structures. Computabilitystudies what can be computed in principle, and has close ties to logic, while complexity studies the time, space, and other resourc…

We feel that discrete calculus allows us to unify many approaches to data analysis and content extraction while being accessible enough to be widely.

Discrete Calculus. With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. Building on a large body of original research at Wolfram Research, the Wolfram Language for the first time delivers a comprehensive system for discrete ...

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity ...

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums.

A plotting program will then draw straight lines between the function values. A discrete representation of a continuous function is, from a programming point of ...

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems ...

• Discrete Exterior Calculus : Discretization of EC for use in computations. Operators defined without global coordinates. Discrete versions of the theorems from smooth theory. DEC is calculus, differential geometry, and tensor analysis on discrete spaces. We aim to preserve, in discrete case, the structure of smooth theory.

Discrete Calculus. A. This appendix is authored by Aslak Tveito. In this chapter we will discuss how to differentiate and integrate functions on a computer.

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

The field of discrete calculus, also known as "discrete exterior calculus", focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space.

Recall (or just nod along) that in normal calculus, we have the derivative and the integral, which satisfy some important properties, such as the fundamental theorem of calculus. Here, we create a similar system for discrete functions. 2 The Discrete Derivative We define the discrete derivative of a function f(n), denoted ∆ nf(n), to be f(n+ ...

be used later on the study of discrete calculus of sequences. 1.1 Difference. The main definition of the calculus of finite differences is ...