Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Espacio de Funciones

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Señales y Sistemas"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Señales y Sistemas"

    Comments:

    "Señales y Sistemas is a Spanish translation of Dr. Rich Baraniuk's collection Signals and Systems (col10064). The translation was coordinated by an an assistant electrical engineering professor […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Espacio de Funciones

Module by: Justin Romberg. E-mail the authorTranslated By: Fara Meza, Erika Jackson

Based on: Function Space by Justin Romberg

Summary: Este modulo da un ejemplo del espacio de las funciones.

También podemos encontrar basis vectores base para espacios vectoriales con exepción de Rn n .

Sea PnPn un espacio vectorial de orden polinomial n-esimo en (-1, 1) con coeficientes reales (verificar que P2P2 es un espacio vectorial en casa).

Ejemplo 1

P2P2 = {todos los polinomios cuadráticos}. Sea b0 t=1 b0 t 1 , b1 t=t b1 t t , b2 t=t2 b2 t t 2 .

b0 t b1 t b2 t b0 t b1 t b2 t genera P2P2, es decir puede escribir cualquier ft P2 f t P2 como ft= α0 b0 t+ α1 b1 t+ α2 b2 t f t α0 b0 t α1 b1 t α2 b2 t para algún αi R αi .

Nota:

P2P2 es de dimensión 3.
ft=t23t4 f t t 2 3 t 4

Base Alternativa b0 t b1 t b2 t=1t12(3t21) b0 t b1 t b2 t 1 t 1 2 3 t 2 1 escribir ft f t en términos de la nueva base d0 t= b0 t d0 t b0 t , d1 t= b1 t d1 t b1 t , d2 t=32 b2 t12 b0 t d2 t 3 2 b2 t 1 2 b0 t . ft=t23t4=4 b0 t3 b1 t+ b2 t f t t 2 3 t 4 4 b0 t 3 b1 t b2 t ft= β0 d0 t+ β1 d1 t+ β2 d2 t= β0 b0 t+ β1 b1 t+ β2 (32 b2 t12 b0 t) f t β0 d0 t β1 d1 t β2 d2 t β0 b0 t β1 b1 t β2 3 2 b2 t 1 2 b0 t ft= β0 b0 t+ β1 b1 t+32 β2 b2 t f t β0 1 2 b0 t β1 b1 t 3 2 β2 b2 t por lo tanto β0 12=4 β0 1 2 4 β1 =-3 β1 -3 32 β2 =1 3 2 β2 1 enotnces obtenemos ft=4.5 d0 t3 d1 t+23 d2 t f t 4.5 d0 t 3 d1 t 2 3 d2 t

Ejemplo 2

ei ω0 nt|n= n ω0 n t es una base para L2 0T L2 0 T , T=2π ω0 T 2 ω0 , ft=n Cn ei ω0 nt f t n Cn ω0 n t .

Calculamos la expansión de coeficientes con

la formula de "cambio de base"

Cn =1T0T(fte(i ω0 nt))dt Cn 1 T t 0 T f t ω0 n t
(1)

nota:

Hay un número infinito de elementos en un conjuto de base, que significan que L2 0T L2 0 T es de dimensión infinita.
Espacios de dimensión-infinita Infinite-dimensional son difíciles de visualizar. Podemos tomar mano de la intuición para reconocer que comparten varias de las propiedades con los espacios de dimensión finita. Muchos conceptos aplicados a ambos (como"expansión de base").Otros no (cambio de base no es una bonita formula de matriz).

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks