Difference between revisions of "Index of notation"
From Maths
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* Real Analysis | * Real Analysis | ||
| Denotes the [[Norm]] of a vector | | Denotes the [[Norm]] of a vector | ||
| + | |- | ||
| + | | <math>\|f\|_{C^k}</math> | ||
| + | | | ||
| + | *Functional Analysis | ||
| + | |This [[Norm]] is defined by <math>\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)</math> - note <math>f^{(i)}</math> is the <math>i^\text{th}</math> derivative. | ||
| + | |- | ||
| + | | <math>\|f\|_{L^p}</math> | ||
| + | | | ||
| + | * Functional Analysis | ||
| + | | <math>\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}</math> - it is a [[Norm]] on <math>\mathcal{C}([0,1],\mathbb{R})</math> | ||
|- | |- | ||
| <math>C([a,b],\mathbb{R})</math> | | <math>C([a,b],\mathbb{R})</math> | ||
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* Real Analysis | * Real Analysis | ||
| It is the set of all functions <math>:[a,b]\rightarrow\mathbb{R}</math> that are [[Continuous map|continuous]] | | It is the set of all functions <math>:[a,b]\rightarrow\mathbb{R}</math> that are [[Continuous map|continuous]] | ||
| + | |- | ||
| + | | <math>C^k([a,b],\mathbb{R})</math> | ||
| + | | | ||
| + | * Functional Analysis | ||
| + | * Real Analysis | ||
| + | | It is the set of all functions <math>:[a,b]\rightarrow\mathbb{R}</math> that are [[Continuous map|continuous]] and have continuous derivatives up to (and including) order <math>k</math><br/> | ||
| + | The unit interval will be assumed when missing | ||
|- | |- | ||
| <math>\ell^p(\mathbb{F})</math> | | <math>\ell^p(\mathbb{F})</math> | ||
Revision as of 02:58, 8 March 2015
Ordered symbols are notations which are (likely) to appear as they are given here, for example [math]C([a,b],\mathbb{R})[/math] denotes the continuous function on the interval [ilmath][a,b][/ilmath] that map to [ilmath]\mathbb{R} [/ilmath] - this is unlikely to be given any other way because "C" is for continuous.
Ordered symbols
These are ordered by symbols, and then by LaTeX names secondly, for example [math]A[/math] comes before [math]\mathbb{A}[/math] comes before [math]\mathcal{A}[/math]
| Expression | Context | Details |
|---|---|---|
| [math]\|\cdot\|[/math] |
|
Denotes the Norm of a vector |
| [math]\|f\|_{C^k}[/math] |
|
This Norm is defined by [math]\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)[/math] - note [math]f^{(i)}[/math] is the [math]i^\text{th}[/math] derivative. |
| [math]\|f\|_{L^p}[/math] |
|
[math]\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}[/math] - it is a Norm on [math]\mathcal{C}([0,1],\mathbb{R})[/math] |
| [math]C([a,b],\mathbb{R})[/math] |
|
It is the set of all functions [math]:[a,b]\rightarrow\mathbb{R}[/math] that are continuous |
| [math]C^k([a,b],\mathbb{R})[/math] |
|
It is the set of all functions [math]:[a,b]\rightarrow\mathbb{R}[/math] that are continuous and have continuous derivatives up to (and including) order [math]k[/math] The unit interval will be assumed when missing |
| [math]\ell^p(\mathbb{F})[/math] |
|
The set of all bounded sequences, that is [math]\ell^p(\mathbb{F})=\{(x_1,x_2,...)|x_i\in\mathbb{F},\ \sum^\infty_{i=1}|x_i|^p<\infty\}[/math] |
