Search results

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

• 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
• 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
• 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

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