Calculus

Mastery approaches with online Internet platforms have been shown to alleviate many students' deficiencies and open the door to higher mathematics. This paper details some current programs using online learning for precalculus courses, and detail how the research ...

CORCORAN ON DERIVATIVES.REPRINT—a review of: Smith, Sheldon R., Incomplete understanding of concepts: the case of the derivative. Mind. 124 (2015), no. 496, 1163—1199.
The article under review, “Incomplete understanding of concepts: the case of the derivative”, hereafter IUC, investigates foundational phenomena spanning the entirety of mathematics: the past and the present. These perennial phenomena involve the increasing clarity of objective mathematical concepts in themselves and the evolving subjective understanding of these concepts by individual mathematicians. But only recently these phenomena have started to attract attention.
They become more vivid as the gap widens between the relative vagueness of ancient mathematics and the relative precision of modern mathematics. Large domains of modern geometry and number theory contain results achieved long ago, sometimes many centuries ago, or at least results having analogs which were achieved earlier. Yet modern mathematics has concepts far more precise than those of ancient mathematics and a modern mathematician has an understanding of mathematical concepts that is far more rigorous than that an ancient mathematician had.
Comparing the clarity and precision of Alfred Tarski’s geometry with the vagueness and imprecision of Euclid’s raises the question of whether the ancient results are literally what are recognized as true today (or only relatively crude forerunners of modern theorems). If the ancient results survived intact, the question concerns how Euclid’s predecessors—whose results Euclid catalogued—achieved results still recognized as true.
This article continues studies of these phenomena as they relate to the concepts of derivative in calculus from Newton and Leibniz to Weierstrass and later analysts.

Con objeto de enfrentar el desarrollo profesional del profesor de matemáticas a nivel universitario, nos planteamos la pregunta ¿cómo fortalecer en un entorno colectivo, la reflexión sobre su práctica del docente universitario de matemáticas? de donde surge el objetivo de estudiar una alternativa de formación para académicos de enseñanza superior, bajo la perspectiva de su reflexión sobre la práctica. Para ello, abordamos el estudio de una sesión de modelación127, llevada a cabo en un evento internacional sobre uso de tecnología. Establecimos referentes teóricos para la organización y definición de terminología, partiendo desde la formación de profesores y continuando con el desarrollo profesional, en él, se consideró la reflexión del profesor, como un elemento que permite comprender mejor al docente y la relación con su práctica.
Con un enfoque cualitativo enfrentamos un estudio descriptivo, utilizando el análisis de contenido para examinar la información, extraída de las transcripciones de la grabación en vídeo de la sesión. Los resultados del análisis, muestran cómo la alternativa de formación propuesta presenta elementos que favorecen la reflexión sobre la práctica de los docentes involucrados.

ABSTRACT
Finance is a major challenge for prosperity of SME’S. Implementing revenue, cost and investments financial strategies are major drivers for improved profitability performance in SME’S. These challenges can be addresses by formulating and effectively implementing financial strategies. In strategic theory, policy dominates strategy by its articulation of the end state and its guidance regarding resources, limitations on actions, or similar considerations. Applying SME resources to achieve profitability in a specific strategic environment over time is crucial. Implementation theory provides a way of integrating information from different agents involved in the financial strategy implementation. It provides a systematic methodology for designing an information exchange process followed by an allocation rule that leads to financial resource allocation decisions that are “optimal” with respect to pre-specified profitability metrics. In Michael Porter’s Theory, Porter cites factors which impede profitability as increased competition, lower barriers to entry, a large number of substitutes, and increased bargaining power of customers and suppliers. Profitability of an SME can be achieved by formulating and implementing financial strategies based on an analysis of these factors through an appropriate configuration and coordination of its value chain activities. Descriptive research studies which describe the characteristics of a particular individual or of a group will be used in the study. A systematic sample of twenty respondents will be selected from a population of one hundred SME respondents in Voi town area in Kenya by picking every third SME respondent recorded starting from the second SME respondent recorded. Questionnaires will be used during interviews to collect primary data from the respondent. The researcher will administer the same questionnaire to ten respondents for pre-testing in a pilot study in Mombasa. Correlation and regression will be used to analyze the extent of relationships between the dependent and independent variables in the study. Inferential statistics, which test for the relationship among the study variables, will be applied. In qualitative data analysis, content analyses will be used and this will involve looking at emerging patterns. The quantitative data findings will be presented using descriptive statistics methods including percentages and frequencies.

Keywords: Financial strategy, profitability, revenue, cost, investment, firm performance and SME challenges.

Among the remarkable sets of vertices of a graph, the independent sets of vertices (acronym IS, other name is the internal stabile sets of vertices) are important, because using them we can solve many classification: in chemistry, health, automobiles traffic, espionage, the chess game, the timetable problem. In this paper, some algorithms to compute the IS family of vertices are improved. A new kind of independents sets of vertices - fuzzy independent sets - related with fuzzy graphs, are defined, and algorithms for finding fuzzy independent sets family are given too.

We deal with a relational model for the demonic se-mantics of programs. The demonic semantics of a while loop is given as a fixed point of a function in-volving the demonic operators. This motivates us to investigate the fixed points of these functions. We give the expression of the greatest ...

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 hallrá 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