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• 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
• 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
• 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

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