Gallery Items tagged Math

On the link between finite difference and derivative of polynomials
The main aim of this paper to establish the relations between forward, backward and central finite (divided) differences (that is discrete analog of the derivative) and partial & ordinary high-order derivatives of the polynomials.
Kolosov Petro

On the quantum differentiation of smooth real-valued functions
Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.
Kolosov Petro

Writing Up Solutions Using LaTeX
A sample document with some code, useful packages, resources, and sample solution writeups to help Phillips Academy math students get started with Overleaf and LaTeX.
Logan Jester

Stagetex - olimpiadi della matematica
Modello di documento latex per la scrittura di soluzioni dei problemi (per la partecipazione agli stage delle olimpiadi di matematica).
Federico Poloni

MAT108 Spring 2018 Homework template
Template for the students of my MAT108 class to submit their homeworks.
Jose Simental Rodriguez

Aplicación del Cálculo Integral para la Solución de Problemáticas Reales
En este artículo se muestra el proceso de solución numérica del ejercicio N°40, página 544, del libro "Cálculo de un variable'', con la finalidad de cumplir los requerimientos para el trabajo final de modelación de la asignatura Cálculo Integral. Por medio de la aplicación de integrales, se determinará la ecuación para el cálculo de la longitud de un cable telefónico y se hallará la altura a la cual debe estar conectado el cable teniendo en cuenta la altura mínima de este respecto al suelo, y la distancia de separación entre ambos postes.
Juan Sebastian Fierro

FSU-MATH2400-Project3-IncludesSampleSolution
In this project, students create a two-dimensional shape with nonuniform density, finds its center of mass, and hang it from a mobile. The various portion of the project address the differences and relationships between computing the center of mass of a discrete set of point masses and a lamina.
Included here is also a sample solution to help students formulate their own well-written solutions. Also, in the LaTeX code are a few comments to address some of the basics of LaTeX and Overleaf.
Sarah Wright

Computer Science Homework Template
CS 405 Analysis of Algorithms homework template.
Hannah Fink

Series Representation of Power Function
In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity
between $m$-order polynomials in \(T\)
\(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)
Kolosov Petro