Difference between revisions of "Index of notation"

Revision as of 02:47, 8 March 2015 (view source) Alec (Talk | contribs) m ← Older edit		Revision as of 02:58, 8 March 2015 (view source) Alec (Talk | contribs) m Newer edit →
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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>

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Revision as of 02:58, 8 March 2015

Ordered symbols are notations which are (likely) to appear as they are given here, for example

$$C([a,b],\mathbb{R})$$ denotes the continuous function on the interval $[a,b]$ that map to $\mathbb{R}$ - 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

$$A$$ comes before $$\mathbb{A}$$ comes before $$\mathcal{A}$$

Expression	Context	Details
$$\|\cdot\|$$	Functional Analysis Real Analysis	Denotes the Norm of a vector
$$\|f\|_{C^k}$$	Functional Analysis	This Norm is defined by $$\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)$$ - note $$f^{(i)}$$ is the $$i^\text{th}$$ derivative.
$$\|f\|_{L^p}$$	Functional Analysis	$$\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}$$ - it is a Norm on $$\mathcal{C}([0,1],\mathbb{R})$$
$$C([a,b],\mathbb{R})$$	Functional Analysis Real Analysis	It is the set of all functions $$:[a,b]\rightarrow\mathbb{R}$$ that are continuous
$$C^k([a,b],\mathbb{R})$$	Functional Analysis Real Analysis	It is the set of all functions $$:[a,b]\rightarrow\mathbb{R}$$ that are continuous and have continuous derivatives up to (and including) order $$k$$ The unit interval will be assumed when missing
$$\ell^p(\mathbb{F})$$	Functional Analysis	The set of all bounded sequences, that is $$\ell^p(\mathbb{F})=\{(x_1,x_2,...)|x_i\in\mathbb{F},\ \sum^\infty_{i=1}|x_i|^p<\infty\}$$

Unordered symbols