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• Calculus exercises: part I
  It's just a limit. But we recognize that this is the derivative of some function. We compare the expression to the formula in the definitio Now, find the derivative of $x\cdot e^{x}$ with PR: above set
  49 KB (8,436 words) - 17:14, 8 March 2018
• Differentiation
  Furthermore, the derivative is defined as a limit. Unlike the limits we saw prior to derivatives, this ...unctions differentiable at a point is differentiable at that point and its derivative is equal to the sum of their derivatives; i.e., for any two functions $f,g$
  82 KB (14,116 words) - 19:50, 6 December 2018
• Calculus of chain maps
  ...nes on ${\mathbb R}_x$ are called ''primal chain functions''. The exterior derivative is also given: ==The derivative of a $0$-chain map is a $1$-chain map==
  41 KB (7,344 words) - 12:52, 25 July 2016
• Applications of integral calculus
  ...-g(c_{i})$. Then, its area is $(f(c_{i})-g(c_{i})) \Delta x_2$. Hence, the total area of the rectangles is: *we represent the total quantity $Q$ as the sum of its values $Q_i$ over simpler, or smaller, regio
  103 KB (18,460 words) - 01:01, 13 February 2019
• Differential calculus of parametric curves
  ==The instantaneous rate of change: derivative== ...es of change and, after the limit, the two components of the vector of the derivative of the curve.
  130 KB (22,842 words) - 13:52, 24 November 2018
• Metric tensor
  ...ay the cells are attached to each other affects the matrix of the exterior derivative: ...ere we start to need geometry is when we move from the first to the second derivative.
  42 KB (7,131 words) - 17:31, 30 November 2015
• Calculus I, the discrete version
  <!--150-->[[image:first derivative and Monotonicity.png| center]] ==The derivative==
  64 KB (11,521 words) - 19:48, 22 June 2017
• Introduction to discrete calculus
  ==The derivative of a $0$-cochain is a $1$-cochain== Even though we are familiar with the derivative of a function as the ''rate of change'', the ''change'' will be initially o
  40 KB (6,983 words) - 19:24, 23 July 2016
• Geometry
  ...ay the cells are attached to each other affects the matrix of the exterior derivative: ...ere we start to need geometry is when we move from the first to the second derivative.
  41 KB (6,928 words) - 17:31, 26 October 2015
• Calculus on cubical complexes
  *the derivative of a function is the ''rate of change'', while *the exterior derivative of a $0$-form is the ''change''.
  36 KB (6,218 words) - 16:26, 30 November 2015
• Discrete forms
  *the derivative of a function is the ''rate of change'', while *the exterior derivative of a $0$-form is the ''change''.
  35 KB (6,055 words) - 13:23, 24 August 2015
• Freshman's introduction to discrete calculus
  <!--150-->[[image:first derivative and Monotonicity.png| center]] ==The derivative==
  42 KB (7,443 words) - 14:18, 1 August 2016
• ODEs
  ...le ''ordinary differential equations (ODEs)'' with respect to the exterior derivative $d$ that have explicit solutions. *the first derivative $f'$ instead of the exterior derivative, and
  47 KB (8,415 words) - 15:46, 1 December 2015
• Several variables
  ...e time is in the first column progressing from $0$ every $.05$. The second derivative is in the next, $0$ and $-32$, respectively. In the next column, the initia A ''pattern'' is clear: growth by $2$. We have the total of six (linear) functions!
  76 KB (13,017 words) - 20:26, 23 February 2019
• Metric complexes
  ...o each other affects the matrix of the boundary operator (and the exterior derivative): that is closed: $A_N=A_0$. The ''total curvature'' of curve $C$ is the sum of the curvatures at the vertices (exce
  35 KB (5,871 words) - 22:43, 7 April 2016
• Tangent bundles
  We now combine all the tangent spaces into one total tangent space. It contains all possible directions in each location: each t The total work over a path in the complex is the ''line integral''<!--\index{line int
  16 KB (2,753 words) - 13:55, 16 March 2016
• The integral
  \text{the derivative }&\text{ the integral}\quad\\ ==The total value of a function: the Riemann sum==
  66 KB (11,473 words) - 21:36, 19 January 2019
• Applications of differential calculus
  Warning: the method fails when it reaches a point where the derivative is equal to (or even close to) $0$. The most important use of the latter notation is in the definition of the derivative:
  59 KB (10,063 words) - 04:59, 21 February 2019
• Functions of several variables OLD
  To define [[derivative]]s we need limits and for [[limits]] we need to understand better the [[top These two cases lead to the concept of [[partial derivative]]s.
  34 KB (5,636 words) - 23:52, 7 October 2017
• PDEs
  ...portion $h$, dependent on the presumed length of the time interval, of the total amount is shared. ...of the ODE of population growth and decay -- with respect to the exterior derivative $d_t$ over time. This time, however, for each cell there are four adjacent
  44 KB (7,469 words) - 18:12, 30 November 2015

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