Cálculo Diferencial e Integral unidos por el Teorema Fundamental del Cálculo

Start Date: 07/05/2020

Course Type: Common Course

Course Link: https://www.coursera.org/learn/calculo-diferencial

Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.

About Course

Los cursos de Cálculo Diferencial y Cálculo Integral tradicionalmente se ofrecen separados y respetando ese orden. El primero estudia la derivada, y el segundo, la integral, siendo este momento en el que aparece el Teorema Fundamental del Cálculo (TFC) para establecer la relación entre ambos conceptos. En el presente curso vamos a hacer una diferencia: introduciremos la derivada y la integral como conceptos relacionados desde un principio. Vamos a iniciar con la interpretación del Teorema Fundamental del Cálculo, con esto nos referimos a descubrir su significado real en la solución de problemas. Llegaremos a asociar con él la actividad práctica de calcular el valor de una magnitud que está cambiando. Habiendo realizado esta interpretación, los conceptos de derivada e integral se verán relacionados desde un principio, lo que te permitirá predecir el valor de una magnitud que está cambiando. Las nociones fundamentales de derivada e integral las identificaremos con las ideas de “razón de cambio” y de “acumulación del cambio”, y el TFC nos proveerá de la estrategia de solución. Recordarás que la Matemática Elemental incluye el Álgebra, la Geometría y la Geometría Analítica. Podemos decir que éstas son Matemáticas que estudian lo estático. En cambio, la Matemática Superior, que incluye el Cálculo, estudia lo dinámico. Con el Cálculo se inicia el estudio del cambio, una realidad presente en nuestro entorno cotidiano sin duda alguna. Costos, temperaturas, poblaciones, velocidades, energías, capitales de inversión, longitudes, etc., son algunos ejemplos de esto. En este curso podrás entender al Cálculo como una estrategia de solución para el estudio del cambio y diferenciarlo de las Matemáticas Elementales, aunque utilice de ellas bastante información. Al finalizar este curso podrás: Describir de qué manera los modelos matemáticos polinomial, exponencial natural, y trigonométricos (seno y coseno), son una construcción que responde a esta práctica de predicción. Los verás a todos ellos surgir de esta práctica cuando una magnitud real particular cumple ciertas condiciones en su “razón de cambio” con respecto a la magnitud de la que depende. Utilizar la introducción de procesos infinitos (¡no imposibles!) en la construcción de la respuesta de predicción, con ello entenderás por qué se habla de Matemática Superior y de un pensamiento matemático avanzado. Valorar una forma de pensar diferente, donde nuestro razonamiento matemático trascienda la sola manipulación de fórmulas algebraicas.

Course Syllabus

Abordaremos aspectos relacionados con el diseño y desarrollo del curso. Plantearemos las razones por las cuales ofrecemos un acercamiento a los contenidos del Cálculo Diferencial e Integral bajo una perspectiva que no ha sido contemplada en la enseñanza y aprendizaje tradicional de estos temas. Además, nos familiarizaremos con el uso de diferentes tecnologías digitales como medio para apoyar esta propuesta didáctica.

Deep Learning Specialization on Coursera

Course Introduction

Los cursos de Cálculo Diferencial y Cálculo Integral tradicionalmente se ofrecen separados y respeta

Course Tag

Differential Calculus Integral Calculus Integral Graphical Model

Related Wiki Topic

Article Example
La audacia y el cálculo La audacia y el cálculo () is a 2011 Argentine book by Beatriz Sarlo. It is focused in the history of Argentina from 2003 to 2010, the presidency of Néstor Kirchner and part of the first presidency of Cristina Fernández de Kirchner (still influenced by Néstor Kirchner). Sarlo details the plots used by Néstor Kirchner to increase his political power.
Integral the integral is called an indefinite integral (also known as antiderivative). The fundamental theorem of calculus relates indefinite integrals and definite integrals. There are many extensions of this notation to generalizations of the integral.
Integral The second fundamental theorem allows many integrals to be calculated explicitly. For example, to calculate the integral
Integral The integral is not actually the antiderivative, but the fundamental theorem provides a way to use antiderivatives to evaluate definite integrals.
Integral The integrals discussed in this article are those termed "definite integrals". It is the fundamental theorem of calculus that connects differentiation with the definite integral: if is a continuous real-valued function defined on a closed interval , then, once an antiderivative of is known, the definite integral of over that interval is given by
Colegio Integral El Avila The school Colegio Integral El Avila is located at Centro de Artes Integradas, Urbanizacion Terrazas del Avila, La Urbina Norte, Caracas, Venezuela.
Fundamental representation that there exists a set of "fundamental weights", indexed by the vertices of the Dynkin diagram, such that any dominant integral weight is a non-negative integer linear combinations of the fundamental weights. The corresponding irreducible representations are the fundamental representations of the Lie group. From the expansion of a dominant weight in terms of the fundamental weights one can take a corresponding tensor product of the fundamental representations and extract one copy of the irreducible representation corresponding to that dominant weight.
Fundamental theorem For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus, which are two distinct branches that are not obviously related. Being "fundamental" does not necessarily mean that it is the most basic result. For example, the proof of the fundamental theorem of arithmetic requires Euclid's lemma, which in turn requires Bézout's identity.
Riemann integral In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration.
Fundamental lemma (Langlands program) The fundamental lemma states that an orbital integral "O" for a group "G" is equal to a stable orbital integral "SO" for an endoscopic group "H", up to a transfer factor Δ :
Colegio Integral El Avila The school Colegio Integral El Avila has 200 days of classes.
Colegio Integral El Avila The main services offered by the school Colegio Integral El Avila are:
Integral The most basic technique for computing definite integrals of one real variable is based on the fundamental theorem of calculus. Let be the function of to be integrated over a given interval . Then, find an antiderivative of ; that is, a function such that on the interval. Provided the integrand and integral have no singularities on the path of integration, by the fundamental theorem of calculus,
Pfeffer integral In mathematics, the Pfeffer integral is an integration technique created by Washek Pfeffer as an attempt to extend the Henstock integral to a multidimensional domain. This was to be done in such a way that the fundamental theorem of calculus would apply analogously to the theorem in one dimension, with as few preconditions on the function under consideration as possible. The integral also permits analogues of the chain rule and other theorems of the integral calculus for higher dimensions.
Fundamental theorem of calculus The version of Taylor's theorem, which expresses the error term as an integral, can be seen as a generalization of the fundamental theorem.
Fundamental theorem of calculus The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.
Fundamental discriminant There is a connection between the theory of integral binary quadratic forms and the arithmetic of quadratic number fields. A basic property of this connection is that "D" is a fundamental discriminant if, and only if, "D" = 1 or "D" is the discriminant of a quadratic number field. There is exactly one quadratic field for every fundamental discriminant "D" ≠ 1, up to isomorphism.
Gaussian integral The Gaussian integral, also known as the Euler–Poisson integral is the integral of the Gaussian function "e" over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss. The integral is:
Integral Such an integral is the Lebesgue integral, that exploits the following fact to enlarge the class of integrable functions: if the values of a function are rearranged over the domain, the integral of a function should remain the same. Thus Henri Lebesgue introduced the integral bearing his name, explaining this integral thus in a letter to Paul Montel:
Integral and call this (yet unknown) area the (definite) integral of . The notation for this integral will be