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• Wedge product of continuous forms
  ...e "multi-vectors". For example, the $2$-vectors should be linear on either vector and and be anti-symmetric. ...$3$-dimensional case each $2$-vector $u \wedge v$ corresponds to a regular vector $u \times v$ and that explains the connection discussed above. In the gener
  14 KB (2,417 words) - 18:16, 22 August 2015
• Forms in Euclidean spaces
  *the vector of functions of the location variables and *the vector of the direction variables.
  44 KB (7,778 words) - 23:32, 24 April 2015
• Algebra of differential forms
  The set of such $k$-forms over $R$ is denoted by $\Omega ^k(R)$. It is a vector space. ==The vector space of differential forms==
  11 KB (1,947 words) - 18:14, 22 August 2015
• Homotopy and homotopy equivalence
  ...space'' if it is equipped with a topology with respect to which its vector operations are continuous: '''Exercise.''' Prove that these are topological vector spaces: ${\bf R}^n$, $C[a,b]$. Hint: don't forget about the product topolog
  45 KB (7,738 words) - 15:18, 24 October 2015
• Tensor fields
  ''[[Multilinear forms]]'' of order $k$ over a real [[vector space]] $V$ are [[multilinear]] antisymmetric functions that give us oriented lengths, area, volumes, etc. They constitute a vector space
  2 KB (289 words) - 22:11, 15 July 2014
• Linear algebra in elementary calculus
  ...serves as a [[basis]]. The obvious choice of operations makes $\Phi^*$ a [[vector space]]. We want to show $\Phi^*/_{\sim}$ is a vector space too.
  4 KB (604 words) - 15:52, 27 August 2015
• Discrete calculus article
  ...y of shape and [[algebra]] is the study of generalizations of [[arithmetic operations]]. The word ''calculus'' is a [[Latin]] word, meaning originally "small pe ...rem of calculus''' states that differentiation and integration are inverse operations. More precisely, it relates the difference quotients to the Riemann sums. I
  27 KB (4,329 words) - 16:02, 1 September 2019
• Linear algebra: exercises
  3. Suppose ${\bf C}({\bf R})$ is the vector space of all continuous functions. Let the function $T:{\bf C}({\bf R})\rig *Suppose $V$ is a vector space with operations: $v+w=0$ and $rv=0$ for all $v,w∈V,r∈R$. How many elements does $V$ hav
  5 KB (833 words) - 13:36, 14 March 2018
• Classes of functions
  ...f squaring the input to the next level and combine it with other algebraic operations. A ''quadratic polynomial'' is a function: We have applied the following operations to the ''power functions'', $x,\ x^2,\ x^3,\ …$:
  143 KB (24,052 words) - 13:11, 23 February 2019
• Linear subspace
  It is a [[subspace of vector space]]. ...$V$ is a ''linear subspace'' if $L$ is a vector space with respect to the operations of $V$.
  443 bytes (83 words) - 12:50, 21 April 2013
• Solving systems of linear equations
  There is a vector equation behind this system of linear (scalar) equations. Our vector space is ${\bf R}$, $x,y \in {\bf R}$.
  5 KB (802 words) - 01:38, 6 September 2011
• Tangent bundles
  Then the work $W$ of force $F$ along vector $D$ is defined to be ...int. The set of all possible directions at point $A\in V={\bf R}^2$ form a vector space of the same dimension. It is $V_A$, a copy of $V$, attached to each p
  16 KB (2,753 words) - 13:55, 16 March 2016
• Topology of Surfaces by Kinsey
  ...calculus: More good stuff (even though the presentation is a bit sketchy): vector fields, ODEs, differentiable manifolds, etc. ...here, beyond just the definition of continuity: continuity under algebraic operations, the [[Intermediate value Theorem]], [[sequences]], etc.''
  5 KB (725 words) - 12:30, 9 September 2016
• Algebra on graphs
  ...ons: $ra+sb,\ \forall r,s \in {\bf R}$. Then $\{a,b \}$ is a basis of this vector space and the idea becomes: ...ne as follows. The joints are ordered and these requests are recorded in a vector format, coordinate-wise. For instance, $(1,0,1,0, . . .)$ means: flip the f
  36 KB (6,177 words) - 02:47, 21 February 2016
• Calculus I, the discrete version
  What happens to the differential(s) as we perform algebraic operations with the function(s)? The operations of differentiation and integration “cancel” each other as follows.
  64 KB (11,521 words) - 19:48, 22 June 2017
• Means
  ...roup, the group may have no division. If these are points in a subset of a vector space, the set may be non-convex. '''Theorem.''' Suppose $G$ is a set with two binary operations:
  10 KB (1,914 words) - 03:05, 6 November 2018
• Linear operator
  '''A linear function preserves vector operations:''' '''Theorem 1.''' If $M, L$ are [[vector space]]s and $A: M → L$ is a linear operator, then
  849 bytes (143 words) - 14:25, 30 July 2012
• From Calculus to Cohomology by Madsen
  *11. [[degree of map|Degree]], [[linking numbers]] and [[index of vector field]]s *15. [[Fiber bundles]] and [[vector bundles]]
  1 KB (118 words) - 13:51, 5 October 2012
• Differential forms: course
  [[Calculus 3: course|Calculus 3]] (or preferably [[Vector calculus: course|vector calculus]]), [[Introduction to abstract mathematics: course|proofs]], [[lin *[[Algebraic operations with forms and cohomology]]
  3 KB (421 words) - 14:44, 8 February 2013
• Calculus as a part of topology
  *For every vector and a number, what is their scalar product? *For every ''vector'', what is its length?
  13 KB (2,233 words) - 14:41, 20 February 2015

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