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• Nabla
  ...partial(\ )}{\partial x}+\mathbf{j}\frac{\partial(\ )}{\partial y}+\mathbf{k}\frac{\partial(\ )}{\partial z}</math> ...ok (Vector Analysis and Cartesian Tensors - Third Edition - D E Borune & P C Kendall - which is a good book) distinguishbetween the <math>\nabla</math>s
  1 KB (245 words) - 18:35, 13 February 2015
• Subspace topology
  {{Requires proof|grade=C|msg=Really easy, hence low importance|easy=true}} {{Requires proof|grade=C|msg=Really easy, hence low importance|easy=true}}
  6 KB (1,146 words) - 23:04, 25 September 2016
• Function
  ...is a space with some useful property, this always means {{M|f:A\rightarrow C}}, for example: ...gical space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}} then we may write:
  4 KB (659 words) - 13:01, 19 February 2016
• Norm
  ...'obvious' as if the image of {{M|\Vert\cdot\Vert}} could be in {{M|\mathbb{C} }} then the {{M|\Vert x\Vert\ge 0}} would make no sense. What ordering wou ...langle\cdot,\cdot\rangle:V\times V\rightarrow(\mathbb{R}\text{ or }\mathbb{C})}} induces a ''norm'' given by:
  6 KB (1,026 words) - 20:33, 9 April 2017
• Index of notation
  ...to {{M|\mathbb{R} }} - this is unlikely to be given any other way because "C" is for continuous. | {{M|\mathbb{S}^n}}, {{M|l_2}}, {{M|\mathcal{C}[a,b]}}
  9 KB (1,490 words) - 06:13, 1 January 2017
• Basis and coordinates
  ...one, <math>\{b_1,...,b_n\}</math>, a point {{M|p}} is given by <m>\sum^n_{k=1}a_ib_i</m> and it is said to have coordinates <math>(a_1,...,a_n)</math> ...math> and it is easy to show that this is linear. Let us call this map {{M|K}} and define it as follows:
  9 KB (1,525 words) - 16:30, 23 August 2015
• Smooth manifold
  ...manifolds - John M Lee - Second Edition</ref> {{M|f:M\rightarrow\mathbb{R}^k}} that satisfies: ...such that {{M|f\circ\varphi^{-1}\subseteq\mathbb{R}^n\rightarrow\mathbb{R}^k }} is [[Smooth|smooth]] in the usual sense, of having continuous partial de
  3 KB (413 words) - 21:09, 12 April 2015
• Smooth function
  ...f\circ\varphi^{-1}:\varphi(U)\subseteq\mathbb{R}^n\rightarrow\mathbb{R}\in C^\infty]}} Note that given an {{M|f:M\rightarrow\mathbb{R}^k}} this is actually just a set of functions, {{M|f_1,\cdots,f_k}} where {{M|
  3 KB (560 words) - 16:16, 14 April 2015
• Addition of vector spaces
  '''Operations:''' (given {{M|u_i,v_i\in V_i}} and {{M|c}} is a scalar in {{M|F}}) * <math>c(v_1,\cdots,v_n)=(cv_1,\cdots,cv_n)</math>
  4 KB (804 words) - 18:02, 18 March 2016
• Index of norms and absolute values
  | <math>\|\cdot\|_{C^k}</math> | <math>\|f\|_{C^k}</math>
  1 KB (207 words) - 09:16, 9 June 2015
• Bounded set
  ...\forall a,b\in A[d(a,b)<C]}} - where {{M|C}} is real<ref group="Note">{{M|C\in\mathbb{R}_{\ge 0} }} should do as {{M|0}} could be a bound, I suppose on ...x\in A}} (where {{M|1=x=(x_1,\cdots,x_n)}}) we have {{M|\vert x_i\vert\le K}} for {{M|i\in\{1,\cdots,n\} }}
  2 KB (409 words) - 23:31, 29 October 2016
• Index of spaces
  ...exed as "num" (notice the lower-case) so a space like {{M|C^k}} is under {{C|C_num}}. We do subscripts first, so {{M|A_i^2}} would be under {{C|A _num ^num:2}}
  3 KB (612 words) - 21:06, 29 February 2016
• Borel sigma-algebra
  ! {{M|1=\mathcal{B}^n=\sigma(\mathcal{C})}} - closed<ref name="MIM"/> ...sigma(\mathcal{O})}} and {{M|1=\sigma(\mathcal{O})\subseteq\sigma(\mathcal{C})}} - see '''Claim 1'''
  5 KB (854 words) - 09:25, 6 August 2015
• Classes of continuously differentiable functions
  ...|C^k}} on {{M|U}}, {{M|C^k(U)}} for {{M|U\subseteq\mathbb{R}^n}} and {{M|C^k(\mathbb{R}^n)}} such. ...U\subseteq\mathbb{R}^n}} (where {{M|U}} is [[Open set|open]]) and some {{M|k\ge 0}}, a function of the form:
  3 KB (632 words) - 20:32, 16 October 2015
• Class of smooth real-valued functions on R-n
  * {{M|C^\infty(\mathbb{R}^n)}} {{Note|The conventions concerning the {{M|C^k}} notation are addressed on the page: ''[[Classes of continuously different
  2 KB (259 words) - 23:41, 21 October 2015
• Sandbox
  I \ar[r]^f \ar[d] \ar@{.>}[dr] & J \ar[r]^g & K \\ C \ar@(dr,dl)@2{_{(}->}[r] _a = "a" & D \ar@{_{(}-^{)} }[r]_b = "b" & Y
  695 B (132 words) - 22:15, 26 October 2015
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/1 implies 2
  :* So {{MM|1=\exists C>0\ \forall N\in\mathbb{N}\ \exists n\in\mathbb{N}[n>N\wedge\Vert L(x_n-p)\V ...at {{M|d(x_n,x)>\epsilon}}, we shall later call such an {{M|\epsilon}} {{M|C}} and construct a subsequence out of the {{M|n}}s
  5 KB (1,064 words) - 02:24, 28 February 2016
• Notes:Boundary operator
  * {{M|1=\partial_p:C_p(K)\rightarrow C_{p-1}(K)}} given by {{M|1=\partial_p\sigma:=\partial_p[v_0,\ldots,v_p]=\sum^p_{i=0} ...is a function, {{M|c}}, from the set of oriented {{M|p}}-simplicies of {{M|K}} to {{M|\mathbb{Z} }} such that:
  1 KB (257 words) - 00:29, 8 May 2016
• Notes:Differential (manifolds)
  * '''Smoothness of a map ({{AKA}}: {{M|C^\infty}}''' - a map, {{M|f:U\subseteq\mathbb{R}^n\rightarrow V\subseteq\mat * '''[[Derivation]]''' - a map, {{M|\omega:C^\infty(M)\rightarrow\mathbb{R} }} that is [[linear map|linear]] and satisfi
  4 KB (716 words) - 14:24, 16 May 2016
• Notes:Mean value theorem
  ** {{M|\exists c\in(a,b)}} such that {{MM|1=f'(c)=\frac{f(a)-f(b)}{b-a} }} ...row\mathbb{R} \in}} [[Classes of continuously differentiable functions|{{M|C^1}} - the class of functions with continuous partial derivatives]]. Let {{M
  3 KB (529 words) - 08:07, 4 June 2016