Search results

Create the page "Differentiable form" on this wiki! See also the search results found.

• Discrete forms and cochains
  ...intervals or, moreover, of $1$-''chains''. We can see this idea in the new form of the additivity property: ...s. The form on the left is what we call the ''exterior derivative'' of the form on the right.
  34 KB (5,619 words) - 16:00, 30 November 2015
• Topology Illustrated -- Index
  *[[cubical form|cubical form]] *[[differentiable form|differentiable form]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Modelling with discrete vector fields and forms
  where $f:R \to R$ is continuous and $x:I \to R$ is differentiable on an open interval $I$. The equation has to be satisfied for all $t \in I$ ...ut $dx$ its [[exterior derivative]], a $1$-form, and $dt$ the constant $1$-form.
  9 KB (1,561 words) - 16:06, 27 August 2015
• Calculus exercises: advanced
  *Solve the following system, expressing the solution in vector form: $$\begin{array}{lll}x_2-x_3=1,\\x_1+x_2+x_3=2.\end{array}$$ **c. If the partial derivatives exist then the function is differentiable.
  14 KB (2,538 words) - 18:35, 14 October 2017
• Applications of differential calculus
  These two sequences of numbers form a sequence of intervals: Thus to compare two functions $f$ and $g$, at infinity or at a point, we form a fraction from them and evaluate the limit of the ratio:
  59 KB (10,063 words) - 04:59, 21 February 2019
• Discrete differential forms
  ...$f$ is [[continuous]]. But if $b > 1 + \frac{a}{2} \pi$, $f$ is nowhere [[differentiable]]. (For another example, consider the issue of [[lengths of curves]] in the | $0$-form
  10 KB (1,471 words) - 12:50, 12 August 2015
• Mean Value Theorem
  ...rem ([[Mean Value Theorem]]).''' Let $[ a, b ] \subset D(h)$, where $h$ is differentiable on $( a, b )$ and $h$ is continuous on $[ a, b ]$. Then ...f which isn't true. This is what it does and does not say about a function differentiable at $X=C$:
  7 KB (1,171 words) - 20:28, 10 July 2018
• Integration of differential forms of degree 0 and 1
  '''Definition:''' Given a $0$-form $\varphi$, the ''integral of the form $\varphi$ over oriented $0$-manifold'' $M=\{p\}$ is: *$0$-form $=$ number assigned to each vertex.
  12 KB (1,906 words) - 17:44, 31 December 2012
• Tangent bundles and differential forms
  Recall, a continuous $1$-form in ${\bf R}^3$ is a function ...$(dx,dy,dz)$. The function is [[linear operator|linear]] on $dx,dy,dz$, [[differentiable]] on $x,y,z$.
  6 KB (1,177 words) - 15:53, 5 November 2012
• Convergence of the discrete to the continuous
  *right then down: we acquire a $0$-form $g$ by sampling function $f$, and then we acquire $dg$ by taking the differ ...he derivative $f'$ of $f$, and then we find the exterior derivative (a $1$-form) $dg$ by integrating $f'$ on the segments:
  21 KB (3,664 words) - 02:02, 18 July 2018
• Calculus I, the discrete version
  ...e domain and a new edge for each node. Together, these new nodes and edges form a new copy of the domain. [[image:form and its dual.png| center]]
  64 KB (11,521 words) - 19:48, 22 June 2017
• Continuous vs discrete differential forms
  ...hat, continuous and discrete forms are very similar in the sense that they form vector spaces that behave similarly. ...on we need to be able to match two very different entities -- a continuous form and a discrete one -- one by one. Let's review what they are.
  9 KB (1,483 words) - 13:54, 13 April 2013
• Systems of ODEs
  provided $x=x(t),\ y=y(t)$ are differentiable at $t$ and $u=f(x,y),\ v=g(x,y)$ are continuous at $(x(t),y(t))$. ...ir of functions $x=x(t)$ and $y=y(t)$ (a parametric curve) with either one differentiable on an open interval $I$ such that for every $t$ in $I$ we have:
  63 KB (10,958 words) - 14:27, 24 November 2018
• Closed and exact forms
  ...(Topological property of exterior derivative).''' If $\varphi$ is a $C^2$-form in $\Omega ^k({\bf R}^n)$, then $d_{k+1}(d_k \varphi)=0$ (we can also write ...uct]] and $A=A(x^1,...,x^n)$ is a coefficient function, twice continuously differentiable. Then, using the definition of exterior derivative and its formula for $0$-
  9 KB (1,423 words) - 20:53, 13 March 2013
• Transformations
  The four coefficients of $x,y$ form the first table: Now form a matrix:
  46 KB (7,625 words) - 13:08, 26 February 2018
• Manifolds model a curved universe
  ...al "generically". They are usually required to be [[continuous]] or even [[differentiable]]. Recall $y = f(x)$ is a $0$-form and $dy=f'(x)dx$ is a $1$-form.
  10 KB (1,588 words) - 17:11, 27 August 2015
• Extrema of functions of several variables
  ...[[First derivative test]]).''' Suppose $a$ is a local extreme point of a [[differentiable function]] $f$. Then which form a line.
  9 KB (1,511 words) - 16:07, 17 August 2011
• Differentiation without limits: part 1
  : for any [[differentiable function]] $f\cdot g$ wrt $x$. : for differentiable $f$ and $g$.
  6 KB (1,004 words) - 16:00, 2 May 2011
• Integration
  ...aled versions of the old ones. Let's recast this statement in the integral form. ...ched versions of the old ones. Let's recast this statement in the integral form:
  69 KB (11,727 words) - 03:34, 30 January 2019
• Properties of the exterior derivative
  where $A,B$ are continuously differentiable functions and $dX,dY$ are basis elements of $ \Omega^k,\Omega^m$ respective '''Theorem.''' $d(d\varphi) = 0$ for any $C^2$-form $\varphi \in \Omega^k$.
  8 KB (1,539 words) - 18:17, 22 August 2015

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)