El documento explica los conceptos básicos de las desigualdades y los intervalos. Define desigualdades absolutas y relativas. Presenta cuatro teoremas sobre las propiedades de las desigualdades. Describe intervalos acotados y no acotados, incluyendo intervalos cerrados, abiertos y semicerrados. Incluye ejemplos de cómo resolver desigualdades y aplicar los conceptos a un problema de costos y ventas.
1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.
Esta presentación es un pequeño esbozo de los productos notables y los casos de factorización, lo cual debe estar acompañado de una buena práctica de resolución de ejercicios. Se recomienda consultar la bibliografía expuesta al final de la presentación. Deben descargar la presentación para ver los productos notables y los casos de factorización que aparecen en las tablas.
Using implicit differentiation we can treat relations which are not quite functions like they were functions. In particular, we can find the slopes of lines tangent to curves which are not graphs of functions.
Este documento trata sobre los fundamentos básicos de los polinomios. Explica qué son las expresiones algebraicas y los diferentes tipos como monomios, binomios, trinomios y polinomios. También describe las partes de un monomio como el coeficiente, la parte literal y el grado. Por último, cubre operaciones básicas con polinomios como suma, resta, multiplicación y factorización.
Las funciones polinómicas se clasifican según su grado en constante, lineal, cuadrática o de grado superior. Son continuas y su dominio son los números reales. Se pueden factorizar utilizando métodos como el factor común o trinomio cuadrado perfecto. Para graficar una función polinómica se determinan sus raíces, intervalos de positividad y negatividad, y se expresa su fórmula de manera factorizada.
This document provides information about quadratic equations including:
1) It defines a quadratic equation as a polynomial equation of the second degree in the general form of ax2 + bx + c = 0, where a ≠ 0.
2) It discusses the importance of quadratic equations, noting that the term "quadratic" comes from the variable being squared (x2) and that a quadratic equation is a trinomial expression with three terms.
3) It presents the method of factorization to solve quadratic equations, showing that if ax2 + bx + c = (rx + p)(sx + q) = 0, then the solutions are x1 = -p/r and x2 = -q/s
1) The document defines different types of polynomials including linear, quadratic, and cubic polynomials. It gives examples of each type.
2) Key information about polynomials includes that the degree refers to the highest power of the variable, and that a polynomial's zeros are the values where it equals 0.
3) Properties of polynomial zeros are discussed, such as that a linear polynomial has 1 zero, a quadratic polynomial has up to 2 zeros, and a cubic polynomial has up to 3 zeros. Relations between coefficients and zeros are also presented.
El documento explica los conceptos básicos de las desigualdades y los intervalos. Define desigualdades absolutas y relativas. Presenta cuatro teoremas sobre las propiedades de las desigualdades. Describe intervalos acotados y no acotados, incluyendo intervalos cerrados, abiertos y semicerrados. Incluye ejemplos de cómo resolver desigualdades y aplicar los conceptos a un problema de costos y ventas.
1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.
Esta presentación es un pequeño esbozo de los productos notables y los casos de factorización, lo cual debe estar acompañado de una buena práctica de resolución de ejercicios. Se recomienda consultar la bibliografía expuesta al final de la presentación. Deben descargar la presentación para ver los productos notables y los casos de factorización que aparecen en las tablas.
Using implicit differentiation we can treat relations which are not quite functions like they were functions. In particular, we can find the slopes of lines tangent to curves which are not graphs of functions.
Este documento trata sobre los fundamentos básicos de los polinomios. Explica qué son las expresiones algebraicas y los diferentes tipos como monomios, binomios, trinomios y polinomios. También describe las partes de un monomio como el coeficiente, la parte literal y el grado. Por último, cubre operaciones básicas con polinomios como suma, resta, multiplicación y factorización.
Las funciones polinómicas se clasifican según su grado en constante, lineal, cuadrática o de grado superior. Son continuas y su dominio son los números reales. Se pueden factorizar utilizando métodos como el factor común o trinomio cuadrado perfecto. Para graficar una función polinómica se determinan sus raíces, intervalos de positividad y negatividad, y se expresa su fórmula de manera factorizada.
This document provides information about quadratic equations including:
1) It defines a quadratic equation as a polynomial equation of the second degree in the general form of ax2 + bx + c = 0, where a ≠ 0.
2) It discusses the importance of quadratic equations, noting that the term "quadratic" comes from the variable being squared (x2) and that a quadratic equation is a trinomial expression with three terms.
3) It presents the method of factorization to solve quadratic equations, showing that if ax2 + bx + c = (rx + p)(sx + q) = 0, then the solutions are x1 = -p/r and x2 = -q/s
1) The document defines different types of polynomials including linear, quadratic, and cubic polynomials. It gives examples of each type.
2) Key information about polynomials includes that the degree refers to the highest power of the variable, and that a polynomial's zeros are the values where it equals 0.
3) Properties of polynomial zeros are discussed, such as that a linear polynomial has 1 zero, a quadratic polynomial has up to 2 zeros, and a cubic polynomial has up to 3 zeros. Relations between coefficients and zeros are also presented.
1) El documento introduce conceptos básicos de vectores en R2 y R3, incluyendo la suma y producto escalar de vectores. 2) Explica la distancia entre dos puntos en R2 y R3 usando el módulo del vector entre los puntos. 3) Describe el producto escalar y su interpretación geométrica, incluyendo su relación con el ángulo entre dos vectores.
This document contains a summary of key concepts in polynomials including:
1) Definitions of terms like variable, term, coefficient, degree, constant and zero polynomials.
2) The Remainder Theorem and how it relates the remainder of polynomial division to the factor theorem.
3) The Factor Theorem and how it can be used to determine if a polynomial is a factor of another.
4) Examples of factoring polynomials and using the Factor Theorem.
5) A list of 15 common algebraic identities involving polynomials.
This document discusses key concepts related to derivatives and their applications:
- It defines increasing and decreasing functions and explains how to determine if a function is increasing or decreasing based on the sign of the derivative.
- It introduces the use of derivatives to find maximum and minimum values, extreme points, and critical points of functions.
- Theorems 1 and 2 provide rules for determining if a critical point represents a maximum or minimum.
- Examples are provided to demonstrate finding the intervals where a function is increasing/decreasing, identifying extrema, and determining the greatest and least function values over an interval.
1. A polynomial of degree n can be represented by a general form that is the sum of terms with ax^n, ax^{n-1}, ..., a1x, and a0.
2. The zeroes (or roots) of a polynomial are the values of x that make the polynomial equal to 0. A linear polynomial graphs as a straight line, a quadratic polynomial graphs as a parabola, and a polynomial of degree n can cross the x-axis at most n times.
3. For a quadratic polynomial ax^2 + bx + c, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
This document discusses limits of functions, including infinite limits, vertical and horizontal asymptotes, and the squeeze theorem. It provides definitions and examples of:
- Infinite limits, where the value of a function increases or decreases without bound as the input approaches a number.
- Vertical and horizontal asymptotes, which are lines that a function approaches but does not meet as the input increases or decreases without limit.
- The squeeze theorem, which can be used to evaluate limits where usual algebraic methods are not effective by "squeezing" the function between two other functions with known limits. Examples demonstrate how to apply this theorem.
1) The document introduces concepts related to polynomials including constants, variables, terms, like terms, unlike terms, and different types of polynomials such as monomials, binomials, trinomials, and multinomials.
2) It discusses the degree of polynomials including linear, quadratic, and cubic polynomials. It also covers the value and zeros of polynomials.
3) The document explains important polynomial concepts such as the factor theorem, polynomial identities, and important points about zeros of polynomials.
La arcocosecante hiperbólica es la inversa de la cosecante hiperbólica. Tiene dos ramas y cada rama es estrictamente decreciente. La fórmula explícita para la arcocosecante hiperbólica involucra funciones logarítmicas y raíces cuadradas.
- Rolle's theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), with f(a) = f(b), then there exists at least one value c in (a,b) where the derivative f'(c) = 0.
- The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that the average rate of change of f over the interval [a,b] equals the instantaneous rate of change
Un espacio vectorial es el objeto básico de estudio en álgebra lineal. Se define como un conjunto no vacío sobre el cual se definen dos operaciones: la suma y el producto por escalares, que cumplen ciertas propiedades. Algunos ejemplos de espacios vectoriales son Rn y los polinomios Pn. Un subespacio vectorial es un subconjunto de un espacio vectorial que también cumple las propiedades de un espacio vectorial. La dimensión de un espacio vectorial es el número de vectores en cualquiera de sus bases.
The Binomial Theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms follow a predictable pattern based on exponents of the variables a and b and coefficients determined by Pascal's Triangle. The theorem was first discovered by Isaac Newton and can be written as a general formula involving factorials and binomial coefficients. It allows for the easy expansion of binomials without having to manually multiply out each term.
Este documento describe las funciones y sus propiedades fundamentales. Define una función como una relación que asocia cada elemento de un conjunto A con un único elemento de un conjunto B. Explica los conceptos de dominio, rango, tipos de funciones como constante, lineal y cuadrática. Luego, introduce las funciones exponenciales, logarítmicas y sus propiedades como ser crecientes o decrecientes, puntos por los que pasan, dominio y rango. Finalmente, cubre límites como laterales e infinitos y reglas básicas para dividir entre infinito.
Este documento presenta una monografía sobre la estructura de anillo. En el capítulo I se define la estructura de anillo y se presentan ejemplos. Un anillo requiere que la adición forme un grupo abeliano, la multiplicación un semigrupo y que se cumplan las leyes distributivas. En los capítulos II al VIII se definen conceptos relacionados como divisores de cero, dominios de integridad, subanillos, ideales e homomorfismos de anillos. Finalmente, en el capítulo IX se discute la importancia de
14 graphs of factorable rational functions xmath260
The document discusses graphs of rational functions. It defines rational functions as functions of the form R(x) = P(x)/Q(x) where P(x) and Q(x) are polynomials. It describes how vertical asymptotes occur where the denominator Q(x) is zero. The graph runs along either side of vertical asymptotes, going up or down depending on the sign chart. There are four cases for how the graph behaves at a vertical asymptote. The document uses examples to illustrate graphing rational functions and determining vertical asymptotes. It also mentions horizontal asymptotes will be discussed.
This document contains lecture notes on inverse trigonometric functions. It begins with definitions of inverse functions and conditions for a function to have an inverse. It then defines the inverse trigonometric functions arcsin, arccos, arctan, and arcsec and gives their domains and ranges. Examples are provided to illustrate calculating values of the inverse trigonometric functions. The document concludes with a brief discussion of notational ambiguity and an outline mentioning derivatives of inverse trigonometric functions and applications.
The document discusses using sign charts to solve polynomial and rational inequalities. It provides examples of solving inequalities by setting one side equal to zero, factoring the expression, drawing the sign chart, and determining the solutions from the regions with the appropriate signs. Specifically, it works through examples of solving x^2 - 3x > 4, 2x^2 - x^3/(x^2 - 2x + 1) < 0, and (x - 2)/(2/(x - 1)) < 3.
This document provides an introduction to linear algebra concepts through a series of slides. It begins by defining vectors as directed line segments in multiple dimensions that can be represented by matrices. It then covers topics such as vector addition, scalar multiplication, dot products, bases, matrices, matrix operations, and how matrices can represent transformations like scaling, rotation, and translation. Later slides discuss cross products, homogeneous coordinates, and transformations involving multiple matrices. The document aims to build understanding of linear algebra concepts starting from basic definitions and representations of vectors and progressively covering more advanced topics.
Este documento presenta una introducción a los números complejos. Explica que los números complejos se pueden representar en forma binómica como a + bi, donde a es la parte real y b la parte imaginaria. También se pueden representar en forma polar mediante su módulo y argumento. Luego describe operaciones básicas como suma, producto, cociente y potencias para números complejos en forma binómica y polar.
Applications of calculus in commerce and economicssumanmathews
This document contains examples and explanations of key concepts in applying calculus to commerce and economics, including:
1) Cost functions, revenue functions, profit functions, and determining break-even points. An example shows calculating the break-even points for a TV manufacturer.
2) Calculating minimum production needed to ensure no loss, and how changing price affects break-even point.
3) Determining the price needed to ensure no loss when production quantity is fixed.
4) Definitions and examples of average cost, total cost, marginal cost, and finding the output where average cost increases.
5) Deriving a revenue function from a demand function and finding the price and quantity that minimize revenue.
In MATLAB, a vector is created by assigning the elements of the vector to a variable. This can be done in several ways depending on the source of the information.
—Enter an explicit list of elements
—Load matrices from external data files
—Using built-in functions
—Using own functions in M-files
Conosci la figura di uno degli scienziati più importanti che l'umanità abbia mai conosciuto direttamente dal palmo della tua mano, condividi con i tuoi amici la passione per la scienza, consulta le numerose curiosità presenti sul web dedicate alla sua figura, questo e molto altro su "Volta pagina", la prima applicazione interamente dedicata ad Alessandro Volta da oggi nel palmo della tua mano!
Disponibile su AppStore https://itunes.apple.com/it/app/volta-pagina/id625979449?mt=8
1) El documento introduce conceptos básicos de vectores en R2 y R3, incluyendo la suma y producto escalar de vectores. 2) Explica la distancia entre dos puntos en R2 y R3 usando el módulo del vector entre los puntos. 3) Describe el producto escalar y su interpretación geométrica, incluyendo su relación con el ángulo entre dos vectores.
This document contains a summary of key concepts in polynomials including:
1) Definitions of terms like variable, term, coefficient, degree, constant and zero polynomials.
2) The Remainder Theorem and how it relates the remainder of polynomial division to the factor theorem.
3) The Factor Theorem and how it can be used to determine if a polynomial is a factor of another.
4) Examples of factoring polynomials and using the Factor Theorem.
5) A list of 15 common algebraic identities involving polynomials.
This document discusses key concepts related to derivatives and their applications:
- It defines increasing and decreasing functions and explains how to determine if a function is increasing or decreasing based on the sign of the derivative.
- It introduces the use of derivatives to find maximum and minimum values, extreme points, and critical points of functions.
- Theorems 1 and 2 provide rules for determining if a critical point represents a maximum or minimum.
- Examples are provided to demonstrate finding the intervals where a function is increasing/decreasing, identifying extrema, and determining the greatest and least function values over an interval.
1. A polynomial of degree n can be represented by a general form that is the sum of terms with ax^n, ax^{n-1}, ..., a1x, and a0.
2. The zeroes (or roots) of a polynomial are the values of x that make the polynomial equal to 0. A linear polynomial graphs as a straight line, a quadratic polynomial graphs as a parabola, and a polynomial of degree n can cross the x-axis at most n times.
3. For a quadratic polynomial ax^2 + bx + c, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
This document discusses limits of functions, including infinite limits, vertical and horizontal asymptotes, and the squeeze theorem. It provides definitions and examples of:
- Infinite limits, where the value of a function increases or decreases without bound as the input approaches a number.
- Vertical and horizontal asymptotes, which are lines that a function approaches but does not meet as the input increases or decreases without limit.
- The squeeze theorem, which can be used to evaluate limits where usual algebraic methods are not effective by "squeezing" the function between two other functions with known limits. Examples demonstrate how to apply this theorem.
1) The document introduces concepts related to polynomials including constants, variables, terms, like terms, unlike terms, and different types of polynomials such as monomials, binomials, trinomials, and multinomials.
2) It discusses the degree of polynomials including linear, quadratic, and cubic polynomials. It also covers the value and zeros of polynomials.
3) The document explains important polynomial concepts such as the factor theorem, polynomial identities, and important points about zeros of polynomials.
La arcocosecante hiperbólica es la inversa de la cosecante hiperbólica. Tiene dos ramas y cada rama es estrictamente decreciente. La fórmula explícita para la arcocosecante hiperbólica involucra funciones logarítmicas y raíces cuadradas.
- Rolle's theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), with f(a) = f(b), then there exists at least one value c in (a,b) where the derivative f'(c) = 0.
- The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that the average rate of change of f over the interval [a,b] equals the instantaneous rate of change
Un espacio vectorial es el objeto básico de estudio en álgebra lineal. Se define como un conjunto no vacío sobre el cual se definen dos operaciones: la suma y el producto por escalares, que cumplen ciertas propiedades. Algunos ejemplos de espacios vectoriales son Rn y los polinomios Pn. Un subespacio vectorial es un subconjunto de un espacio vectorial que también cumple las propiedades de un espacio vectorial. La dimensión de un espacio vectorial es el número de vectores en cualquiera de sus bases.
The Binomial Theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms follow a predictable pattern based on exponents of the variables a and b and coefficients determined by Pascal's Triangle. The theorem was first discovered by Isaac Newton and can be written as a general formula involving factorials and binomial coefficients. It allows for the easy expansion of binomials without having to manually multiply out each term.
Este documento describe las funciones y sus propiedades fundamentales. Define una función como una relación que asocia cada elemento de un conjunto A con un único elemento de un conjunto B. Explica los conceptos de dominio, rango, tipos de funciones como constante, lineal y cuadrática. Luego, introduce las funciones exponenciales, logarítmicas y sus propiedades como ser crecientes o decrecientes, puntos por los que pasan, dominio y rango. Finalmente, cubre límites como laterales e infinitos y reglas básicas para dividir entre infinito.
Este documento presenta una monografía sobre la estructura de anillo. En el capítulo I se define la estructura de anillo y se presentan ejemplos. Un anillo requiere que la adición forme un grupo abeliano, la multiplicación un semigrupo y que se cumplan las leyes distributivas. En los capítulos II al VIII se definen conceptos relacionados como divisores de cero, dominios de integridad, subanillos, ideales e homomorfismos de anillos. Finalmente, en el capítulo IX se discute la importancia de
14 graphs of factorable rational functions xmath260
The document discusses graphs of rational functions. It defines rational functions as functions of the form R(x) = P(x)/Q(x) where P(x) and Q(x) are polynomials. It describes how vertical asymptotes occur where the denominator Q(x) is zero. The graph runs along either side of vertical asymptotes, going up or down depending on the sign chart. There are four cases for how the graph behaves at a vertical asymptote. The document uses examples to illustrate graphing rational functions and determining vertical asymptotes. It also mentions horizontal asymptotes will be discussed.
This document contains lecture notes on inverse trigonometric functions. It begins with definitions of inverse functions and conditions for a function to have an inverse. It then defines the inverse trigonometric functions arcsin, arccos, arctan, and arcsec and gives their domains and ranges. Examples are provided to illustrate calculating values of the inverse trigonometric functions. The document concludes with a brief discussion of notational ambiguity and an outline mentioning derivatives of inverse trigonometric functions and applications.
The document discusses using sign charts to solve polynomial and rational inequalities. It provides examples of solving inequalities by setting one side equal to zero, factoring the expression, drawing the sign chart, and determining the solutions from the regions with the appropriate signs. Specifically, it works through examples of solving x^2 - 3x > 4, 2x^2 - x^3/(x^2 - 2x + 1) < 0, and (x - 2)/(2/(x - 1)) < 3.
This document provides an introduction to linear algebra concepts through a series of slides. It begins by defining vectors as directed line segments in multiple dimensions that can be represented by matrices. It then covers topics such as vector addition, scalar multiplication, dot products, bases, matrices, matrix operations, and how matrices can represent transformations like scaling, rotation, and translation. Later slides discuss cross products, homogeneous coordinates, and transformations involving multiple matrices. The document aims to build understanding of linear algebra concepts starting from basic definitions and representations of vectors and progressively covering more advanced topics.
Este documento presenta una introducción a los números complejos. Explica que los números complejos se pueden representar en forma binómica como a + bi, donde a es la parte real y b la parte imaginaria. También se pueden representar en forma polar mediante su módulo y argumento. Luego describe operaciones básicas como suma, producto, cociente y potencias para números complejos en forma binómica y polar.
Applications of calculus in commerce and economicssumanmathews
This document contains examples and explanations of key concepts in applying calculus to commerce and economics, including:
1) Cost functions, revenue functions, profit functions, and determining break-even points. An example shows calculating the break-even points for a TV manufacturer.
2) Calculating minimum production needed to ensure no loss, and how changing price affects break-even point.
3) Determining the price needed to ensure no loss when production quantity is fixed.
4) Definitions and examples of average cost, total cost, marginal cost, and finding the output where average cost increases.
5) Deriving a revenue function from a demand function and finding the price and quantity that minimize revenue.
In MATLAB, a vector is created by assigning the elements of the vector to a variable. This can be done in several ways depending on the source of the information.
—Enter an explicit list of elements
—Load matrices from external data files
—Using built-in functions
—Using own functions in M-files
Conosci la figura di uno degli scienziati più importanti che l'umanità abbia mai conosciuto direttamente dal palmo della tua mano, condividi con i tuoi amici la passione per la scienza, consulta le numerose curiosità presenti sul web dedicate alla sua figura, questo e molto altro su "Volta pagina", la prima applicazione interamente dedicata ad Alessandro Volta da oggi nel palmo della tua mano!
Disponibile su AppStore https://itunes.apple.com/it/app/volta-pagina/id625979449?mt=8
A árvore de causas é um método para investigar acidentes/incidentes identificando o encadeamento lógico dos fatos que os provocaram. Ela representa graficamente a sequência de acontecimentos e possíveis causas, desde as mais diretas até as de nível sistêmico, para compreender e prevenir futuros riscos.
Preguntas Taller No 3. segundo corte constitucional colombianoCESARTUTTO24
El documento presenta un cuestionario de 9 preguntas sobre el derecho procesal constitucional y el derecho probatorio constitucional en Colombia para una clase de derecho constitucional colombiano. Las preguntas abarcan temas como la definición del derecho procesal constitucional en Colombia, los mecanismos de protección de la supremacía de la constitución, el control judicial constitucional en diferentes países, la jurisdicción constitucional en Colombia y sus organismos, las funciones del juez constitucional y las diferencias entre procedimiento y proceso constitucional.
The document discusses strategies for engaging students in the classroom. It aims to have participants consider ideas that support student engagement and how to apply these strategies in their own settings. Some challenges to student engagement are discussed, such as a lack of focus, behavioral issues, and struggles for control that can negatively impact learning. Theories around the importance of building positive student relationships and engaging students cognitively, behaviorally, and emotionally are presented. A group activity brainstorms examples of what affects student engagement, and participants are asked to consider strategies for engaging students in their own classrooms.
Yashpal Singh has over 20 years of experience in human resources and administration, including 12 years in HR roles. He is currently the Head of HR and Administration at National Infra Industries Ltd. Previously he held HR leadership positions at Carrier Wheels Pvt Ltd and Bajaj Eco Tech Products Ltd. Singh has expertise in areas such as recruitment, performance management, training, employee engagement, and industrial relations. He holds an MBA in Human Resources and Industrial Relations and is seeking a growth-oriented organization where he can continue enhancing his skills.
Los niños ponen castañas en un mantel para contarlas y ver quién tiene más. Es difícil contarlas todas juntas, así que deciden separarlas y ponerlas en filas para contar mejor. Después de organizar las castañas, descubren que Tomé, Ángela y Evelyn tienen más que los demás porque sus filas dan la vuelta completa al mantel y tienen que empezar otra en el medio. Entre Ángela y Evelyn, Evelyn tiene más porque su fila del medio está completa, mientras que la de Ángela no lo está.
«Branch, Internet, Mobile, Digital» is a study that aims to synthesize and connect some of the most innovative actions that Banks, Fintechs and other actors are undertaking to develop a new model for the financial services.
Views expressed in this presentation are my own.
Este documento describe cómo el autor integró las tecnologías de la información y la comunicación (TIC) en su práctica docente en diferentes áreas como Persona, Familia y Relaciones Humanas y Educación para el Trabajo utilizando laptops XO con estudiantes de secundaria. El autor utilizó las laptops XO para que los estudiantes vean videos, desarrollen fichas de trabajo y se comuniquen entre sí a través de mensajería instantánea para colaborar y construir conocimientos. También usó blogs, elaboración de
Presentazione semplice basata su http://www.infn.it/multimedia/particle/paitaliano/startstandard.html
usata nell'incontro di preparazione della conferenza del prof. Bertolucci del 19 maggio 2012 presso Romero di Albino
La conferenza descrive in modo divulgativo il profondo lavoro mentale che ha portato Maxwell nel
triennio 1861-1863, centocinquant’anni fa, a concepire il modello dei campi partendo dalla ricerca
dell’etere.
La conferenza è stata realizzata dal prof. Luciano De Menna, Università degli Studi Federico II di Napoli, in occasione dell'appuntamento stagionale "Conferenze di stagione" organizzato a maggio 2014 dalla Fondazione C. Fillietroz - Osservatorio Astronomico della Regione Autonoma Valle d'Aosta e Planetario di Lignan in collaborazione con l'Università della Valle d'Aosta - Université de la Vallée d’Aoste.
4. Col termine elettricità si fa riferimento genericamente a
tutti i fenomeni fisici su scala macroscopica che
coinvolgono una delle interazioni fondamentali.
A livello microscopico, tali fenomeni sono riconducibili
all'interazione tra particelle cariche su scala molecolare:
i protoni nel nucleo di atomi o molecole ionizzate, e gli
elettroni.
I tipici effetti macroscopici di tali interazioni sono le
correnti elettriche e l'attrazione o repulsione di corpi
elettricamente carichi.
• NEUTRE • Cariche uguali ( - - ) • Cariche uguali ( + + )• Cariche segno opposto ( + - )
5. I primi studi dei fenomeni risalgono
probabilmente al filosofo greco
Talete, che studiò le proprietà
elettriche dell'ambra, la resina
fossile che se viene sfregata
( attraverso un panno di lana) attrae
altri pezzetti di materia: il suo nome
greco era electron , e da questo
termine deriva la parola
«elettricità».
I greci antichi compresero che
l'ambra era in grado di attrarre
oggetti leggeri, come i capelli, e che
un ripetuto strofinio dell'ambra
stessa poteva addirittura dare
origine a scintille.
Informazioni: uscita didattica
6. Nella pila di Volta i dischi sono sostituiti da due
bacchette formate da metalli diversi (rame e zinco),
chiamate elettrodi, immerse in una soluzione
elettrolitica, cioè una soluzione acquosa di sali o di
acidi che permettono il passaggio della corrente perché
in essa sono presenti particelle cariche elettricamente,
dette ioni.
Ogni elettrodo metallico, si dissocia parzialmente
e cede altri ioni, così si genera una differenza di
potenziale ( d.d.p è la differenza tra l'energia
potenziale elettrica posseduta da una carica nei
due punti a causa della presenza di un campo
elettrico) tra il metallo e la soluzione.
La differenza di potenziale dipende dal metallo
considerato .
Lo zinco che assume il potenziale più negativo
permette il passaggio di una corrente elettrica dal
rame allo zinco quando i due elettrodi sono
collegati da un filo conduttore.
7. L’elettroforo perpetuo è un generatore
elettrostatico in grado di accumulare in
grado di accumulare una quantità di
cariche elettriche in modo discontinuo.
Costituito: da un disco di materiale
conduttore, un manico isolante e da una
superficie in materiale isolante
Funzionamento: la base isolante viene
caricata da un panno di lana attraverso lo
strofinio, dopo di che si appoggia il disco al
piano.
Per induzione, il disco si carica di cariche
positive, a questo punto si tocca con un dito
la parte superiore del disco, in questo modo
lo si mette a terra attraverso il corpo umano
si fa defluire la carica negativa, lasciando il
disco caricato positivamente
8. Il volt è l'unità di misura
derivata Sistema
Internazionale (SI) del
potenziale elettrico e della
differenza di potenziale.
Ha questo nome in onore
di Alessandro Volta, che
nel 1800 inventò la pila
voltaica, la prima batteria
elettrochimica.
Negli anni 1880 il
Congresso Elettrico
Internazionale, approvò il
volt come unità di misura
della forza elettromotrice.
J
C
V =
9. Nell'autunno del 1776 Alessandro Volta
studiò un fenomeno noto anche in epoche
più lontane: si trovava in un stagnante del
fiume Lambro, avvicinando una fiamma alla
superficie si accendevano delle fiammelle
azzurrine.
Alessandro Volta scoprì l'aria infiammabile
nella palude dell'Isolino Partegora , in
località Bruschera (provincia di Varese).
Provando a smuovere il fondo con l'aiuto di
un bastone vide che risalivano delle bolle di
gas e le raccolse in bottiglie.
Diede a questo gas il nome di aria
infiammabile di palude e scoprì che poteva
essere incendiato , sia per mezzo di una
candela accesa , sia mediante una scarica
elettrica; dedusse che il gas si formava nella
decomposizione di sostanze animali e
vegetali
