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• The algebra of cells
  We know how to compute the derivative of the product of, say, three functions. We simply apply the product rule t ...olved and each contains all three, except one of them is replaced with its derivative. Applying the rule for boundaries above will have the exact same effect. Th
  34 KB (5,644 words) - 13:35, 1 December 2015
• Integration in dimension n
  <center>total area of rectangles $= f(c_1) {\Delta}x + f(c_2) {\Delta}x + ... + f(c_k) {\ ...$k$ intervals. Then the volume is the sum of the volumes of the boxes, in total there are $k^n$. Integrate over $B$ to get the $( n + 1 )$-dimensional volu
  33 KB (5,415 words) - 05:58, 20 August 2011
• Calculus of sequences
  ...ay}{|c|}\hline \quad \text{function} \quad \longrightarrow \quad \text{its derivative}. \quad \\ \hline\end{array}$$ and the total amount becomes $\$1010$. After the second year we have the interest:
  113 KB (18,425 words) - 13:42, 8 February 2019
• Calculus II -- Spring 2018
  *Prerequisites: excellent algebra skills, good understanding of limits, the derivative, and the integral, fluent differentiation -- [[Calculus I -- Fall 2017|Calc i.e., the total score is the following weighted average of the five scores:
  12 KB (1,928 words) - 19:15, 12 April 2018
• Wave equation
  Note that for a constant $k$, we are dealing with the second derivative of the $0$-form $u$ with respect to space: Compare it to the second derivative of a $1$-form $U$ with respect to space:
  10 KB (1,775 words) - 02:40, 9 April 2016
• Examples of differential forms
  We will start our exploration with familiar idea of the [[derivative]] from [[calculus 1:_course|calculus 1]]. Consider the two notations for the [[derivative]] at $a$ of $f$:
  5 KB (959 words) - 13:15, 12 August 2015
• Convergence of the discrete to the continuous
  ...we acquire first the derivative $f'$ of $f$, and then we find the exterior derivative (a $1$-form) $dg$ by integrating $f'$ on the segments: '''Exercise.''' Show that, in this case, all the values of the derivative $f'$ of $f$ are the limits of sequences of values of $g_k'$, under the assu
  21 KB (3,664 words) - 02:02, 18 July 2018
• Higher order votes
  After all, the derivative of a monotonic function is either all positive or all negative. ...ch voter's rating vote into a comparison vote, then tally the votes into a total comparison vote, and then finally convert it back to a rating vote. (The la
  41 KB (6,942 words) - 05:04, 22 June 2016
• Calculus I -- Fall 2018
  *Goals: good understanding of limits, the derivative and the integral, fluent differentiation. i.e., the total score is the following weighted average of the five scores:
  8 KB (1,184 words) - 17:55, 29 October 2018
• Calculus exercises: advanced
  *Find the matrix of the total derivative of $F(x,y)=(x\sin y,x-y)$ at $(1,0).$ ...n such that the matrix of $F'(0,0)$ is the identity matrix. Find the total derivative of the vector function $H(x,y)=F(xy-1,x+y-2)$ at $(1,1)$.
  14 KB (2,538 words) - 18:35, 14 October 2017
• Calculus I -- Fall 2016
  *Goals: good understanding of limits, the derivative and the integral, fluent differentiation *Grade Breakdown: TOTAL $= .05 \times P + .25\times (Q + H) + .20\times FP + .20\times M + .30\time
  11 KB (1,671 words) - 23:11, 13 December 2016
• Calculus I -- Spring 2017
  *Goals: good understanding of limits, the derivative and the integral, fluent differentiation *Grade Breakdown: TOTAL $= .05 \times P + .25\times (Q + H) + .20\times FP + .20\times M + .30\time
  12 KB (1,803 words) - 20:50, 1 May 2017
• Social choice
  After all, the derivative of a monotonic function is either all positive or all negative. ...nt the web as a directed graph and let $E$ be the set of edges and $N$ the total number of nodes in the graph. Then the PageRank is defined by the recursive
  47 KB (8,030 words) - 18:48, 30 November 2015
• The algebra of oriented cubes
  Warning: A common mistake in elementary calculus is to assume that the derivative of the product is the product of the derivatives. Don't make a similar mist ...-\index{chain groups}--> $L$ and we call, within this section, $C_k$ the ''total $k$th chain group''.
  32 KB (5,480 words) - 02:23, 26 March 2016
• Divergence
  ...ow of adjacent pieces cancel each other, the total of these numbers is the total amount of liquid leaving the region. ...em of Calculus]]. Thus, the divergence is simply a generalization of the [[derivative]].
  2 KB (385 words) - 20:18, 28 August 2011
• Calculus III -- Fall 2017
  *Prerequisites: excellent algebra skills, good understanding of the derivative and the integral, fluent differentiation and integration. i.e., the total score is the following weighted average of the five scores:
  10 KB (1,596 words) - 13:34, 27 November 2017
• Wave equation from Maxwell equations
  *$J$: ''total current density'' (including both free and bound current); *$d$ and $d^*$ are the [[exterior derivative]] of the primal and the dual complex respectively,
  4 KB (655 words) - 14:51, 13 July 2012
• Modern Thermodynamics by John Denker
  ...the word comes from: this k-form is (or is not) ''exactly'' the [[exterior derivative]] of some (k-1)-form. ...for [[differential form]]s of higher degree when we deal with the exterior derivative not gradient. Why not simply call it a "1-form that isn't exact"?
  8 KB (1,251 words) - 03:54, 29 March 2011
• Computing integrals
  ...iation exercises -- use properties and the list of derivatives (7 items in total). We don't recognize $\sin (x^{2})$ as the derivative of any function we know.
  7 KB (1,114 words) - 18:15, 21 July 2011
• Calculus II -- Fall 2018
  *Prerequisites: excellent algebra skills, good understanding of limits, the derivative, and the integral, fluent differentiation -- [[Calculus I -- Fall 2017|Calc i.e., the total score is the following weighted average of the five scores:
  3 KB (431 words) - 17:55, 29 October 2018

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