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• Partial differential equations
  ...ote that the total amount of heat in the rod remains the same (seen under “total” in the spreadsheet shown above). ...ortion, $k$, dependent on the presumed length of the time interval, of the total amount is exchanged.
  53 KB (9,682 words) - 23:19, 18 November 2018
• Functions of several variables: derivatives and integrals
  ==The derivative of a function of several variables== '''Definition.''' The ''partial derivative of $z=f(X)=f(x_1,...,x_n)$ with respect $x_k$ at'' $X=A=(a_1,...,a_n)$ are
  42 KB (6,904 words) - 15:15, 30 October 2017
• Combinatorial cell maps
  This is a vertical flip; there are also the horizontal and diagonal flips, a total of $4$. Only these four axes allow condition (A) to be satisfied. $\square$ is the (total) ''chain map''<!--\index{chain map}--> generated by $f$.
  31 KB (5,330 words) - 22:14, 14 March 2016
• Calculus Illustrated
  *Chapter 3. The derivative 4 The limit of the difference quotient: the derivative
  16 KB (1,933 words) - 19:50, 28 June 2021
• Diffusion equation
  ...portion $h$, dependent on the presumed length of the time interval, of the total amount is exchanged. The two images below are the initial state (a single i ...of the ODE of population growth and decay -- with respect to the exterior derivative $d_t$ over time. For each cell there are four adjacent cells and four tempe
  35 KB (5,917 words) - 12:51, 30 June 2016
• Vector fields
  Assuming a fixed mass, the total force gives us our acceleration. We to compute: What is the total flow along this “staircase”? We simply add the values located on these
  91 KB (16,253 words) - 04:52, 9 January 2019
• Calculus exercises: part III
  and its derivative equals Find the directional derivative $D_v f(1,0,1)$, where
  46 KB (8,035 words) - 13:50, 15 March 2018
• Integration
  But we don't recognize $\sin (x^{2})$ as the derivative of any function we know... *the derivative of the “inside” function is present as a factor.
  69 KB (11,727 words) - 03:34, 30 January 2019
• Geometric complexes
  The expression can be understood as: the total flux of $a$ across a region of area $1$ on $a^\star$. ...ve” is always trivial. Instead, one can define the “Hodge-dualized” second derivative computed following these four steps:
  20 KB (3,354 words) - 17:37, 30 November 2015
• More metric complexes
  The expression can be understood as the total flux of $a$ across a region of area $1$ on $a^\star$: ...ve” is always trivial. Instead, one can define the “Hodge-dualized” second derivative computed following these four steps:
  21 KB (3,445 words) - 13:53, 19 February 2016
• Transformations
  ...r pound. How much of each do you need to have $6$ pounds of blend with the total price of $\$14$? ...the Kenyan coffee and let $y$ be the weight of Colombian coffee. Then the total price of the blend is $\$ 14$. Therefore, we have a system:
  46 KB (7,625 words) - 13:08, 26 February 2018
• Material derivative
  The ''material derivative'' is the [[rate of change]] of some physical quantity ([[heat]], or [[momen ...d the physical quantity is the temperature of the fluid. Then the material derivative describes the temperature evolution of a certain fluid parcel in time, as i
  2 KB (388 words) - 21:31, 17 July 2012
• Diffusion
  *$d_t$ is the exterior derivative with respect to time (just the difference since the dimension is $1$); and *$d_x$ is the exterior derivative with respect to location.
  39 KB (6,850 words) - 15:29, 17 July 2015
• Differential equations
  ...opulation $\Delta y$ is proportional to $y$... and $T-y$, where $T$ is the total possible population: In the meantime, the derivative, if any, would satisfy the following:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Vector and complex variables
  ...r pound. How much of each do you need to have $6$ pounds of blend with the total price of $\$14$? ...the Kenyan coffee and let $y$ be the weight of Colombian coffee. Then the total price of the blend is $\$ 14$. Therefore, we have a system:
  113 KB (18,750 words) - 02:33, 10 December 2018
• Discrete forms and cochains
  <center>''a function on the right and its derivative is on the left''. </center> ...as differential forms. 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
• Affine approximation
  ...linear map evaluated at $x-a$. This linear map $L_a$ is called the ''total derivative of $f$ at $x = a$''. Then, the total derivative
  7 KB (1,162 words) - 03:25, 22 August 2011
• Forms
  We collect the tangent spaces into the (dimension $1$) ''total tangent space'' of $K$: Then $\varphi$ is a function on the total tangent space,
  13 KB (2,459 words) - 03:27, 25 June 2015
• Discrete calculus article
  ..., however, can take the squaring function as an input. This means that the derivative takes all the information of the squaring function—such as that two is se ...me. For example, travelling a steady 50&nbsp;mph for 3 hours results in a total distance of 150 miles. In the diagram on the left, when constant velocity
  27 KB (4,329 words) - 16:02, 1 September 2019
• Calculus I -- Fall 2017
  *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:
  13 KB (2,075 words) - 13:35, 27 November 2017

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