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
• Tangent bundle
  ...which is a [[differential form]] of degree $1$, for the same purpose. This form is ''defined'' on the tangent vectors to the domain manifold. We now invest ...n. Let's parametrize $C$ as $p \colon [a,b] \rightarrow C$, where $p$ is [[differentiable]].
  5 KB (859 words) - 02:33, 22 January 2013
• First derivative test
  ...st derivative test in dim n).''' Suppose a is a local extreme point of a [[differentiable function]] f. Then which form a line.
  3 KB (438 words) - 19:02, 7 August 2010
• Functions of several variables OLD
  ...restriction of $f$ to $L, D(g) = L$. Now every element $v$ in $L$ has the form The idea comes from the fact that if you zoom in on the graph of a [[differentiable function]], it looks like a straight line.
  34 KB (5,636 words) - 23:52, 7 October 2017
• Euler and Lefschetz numbers
  Recall that we have $n$ commodities freely traded with possible prices that form a ''price vector'' $p=(p_1,...,p_n),$ at each moment of time. Then all posi under some norm so that the new prices form the $n$-simplex $\sigma$.
  41 KB (7,169 words) - 14:00, 1 December 2015
• Calculus on graphs
  ...by $C^0(G)$ and $C^1(G)$ respectively (not to be confused with the set of differentiable functions). ...cochains are called ''discrete differential forms''<!--\index{differential form}-->, to be discussed later.
  16 KB (2,578 words) - 00:14, 18 February 2016
• Linear approximations
  Assume $f$ is [[differentiable]] at $x=a$. In that case, when you zoom in on the point, the tangent line w [[Point-slope]] form:
  2 KB (384 words) - 15:44, 2 May 2011
• More about manifolds
  ...half-disk but, when it's glued to its antipodal point, the two half-disks form a whole disk. Let's classify the level sets of a twice [[differentiable]] function.
  9 KB (1,542 words) - 19:58, 21 January 2014
• Affine approximation
  The idea comes from the fact that if you zoom in on the graph of a [[differentiable function]], it looks like a straight line. Let $f: {\bf R}^n {\rightarrow} {\bf R}^m$. What is the form of $T$?
  7 KB (1,162 words) - 03:25, 22 August 2011
• Modelling motion on manifolds
  ...o {\bf R}^n$ is a continuous [[vector field]] and $x:I \to {\bf R}^n$ is a differentiable [[parametric curve]] defined on an open interval $I$. and a vector-valued $0$-form.
  2 KB (377 words) - 17:13, 27 August 2015
• A new look at continuity
  '''Exercise.''' In addition to being continuous, $f(x)=x^2$ is also differentiable. How does that help with the accuracy issue? Hint: there is a simple depend ...to algebra, it will explain how these pieces fit together ''globally'' to form components<!--\index{path-component}-->, holes<!--\index{holes}-->, voids<!
  17 KB (2,946 words) - 04:51, 25 November 2015
• Applications of integral calculus
  Therefore, the balance equation has this form: Now, something a bit more specific. What if these points form the graph of a function $y=f(x)$ defined at the nodes of a partition of $[a
  103 KB (18,460 words) - 01:01, 13 February 2019
• Calculus exercises: part III
  *Find the reduced row echelon form of the following system of linear equations. What kind of set is its soluti ...${\bf R}^2$ that are orthogonal to $<-1,3>$. Write the set in the standard form of a line through the origin.
  46 KB (8,035 words) - 13:50, 15 March 2018
• Vector integrals
  ...exists (it does when $F$ is [[continuous]] and the curve is continuously [[differentiable]]), then we define the ''line integral'' as this limit (here $F \cdot V ds$ is a [[differential form]]).
  15 KB (2,545 words) - 19:47, 20 August 2011
• Linear algebra: test 2
  #Suppose $V$ is the space of differentiable at $0$ functions of two variables. Suppose $A:V\longrightarrow \mathbf{R}^{ Form a matrix from these columns.
  4 KB (583 words) - 01:13, 12 October 2011
• Matrices as functions
  *2. $\frac{d}{dx} \colon C^1({\bf R}) \rightarrow ?$, (from the [[differentiable]] functions to what?) ...row {\bf R}$: $f'(a)=3$, or $\frac{dy}{dx}=3$, or $dy=3dx$ ([[differential form]]).
  13 KB (2,187 words) - 22:17, 9 September 2011
• Geometry in calculus
  This looks very much like the definition of a $2$-form except it's ''symmetric not antisymmetric''! if $C$ is parametrized by a differentiable function $p:[a,b] \rightarrow {\bf R}^n$. We can also compute the [[curvatu
  9 KB (1,604 words) - 18:08, 27 August 2015
• Homology as an equivalence relation
  ...and $B$ are ''homologous'' if there is a surface $S$ such that $A$ and $B$ form its boundary. *$F$ is differentiable on $X$,
  21 KB (3,530 words) - 19:54, 23 June 2015
• Homology classes
  ...and $B$ are ''homologous'' if there is a surface $S$ such that $A$ and $B$ form its boundary. *$F$ is differentiable on $X$,
  21 KB (3,581 words) - 15:51, 28 November 2015
• Homotopy
  ...this surface. The homotopy above is piece-wise linear and the one below is differentiable: '''Exercise.''' Prove that pointed spaces and pointed maps form a category.
  46 KB (7,846 words) - 02:47, 30 November 2015
• Compact spaces
  ...$\alpha$. choose a single element of $\gamma$ that contains it. These sets form a finite subcover of $\gamma$. $\blacksquare$ Hint: To understand the concept, limit the set to differentiable functions with the derivatives between, say, $-1$ and $1$.
  19 KB (3,207 words) - 13:06, 29 November 2015
• Derivative as a limit
  The [[point-slope form]] of the line: We say that $f$ isn't ''[[differentiable]]''.
  5 KB (857 words) - 13:57, 25 May 2011
• Vector calculus: review
  ...s of a linear space. (b) Show that the vectors $(1,0,0), (1,1,0), (1,1,1)$ form a basis of ${\bf R}^3$. #Let $F$ be a differentiable parametric curve. If $F^{\prime}(t)$ is perpendicular to $F(t)$ for all $t,
  7 KB (1,394 words) - 02:36, 22 August 2011

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