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• Several variables
  First, the ''sequences''. ...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
  76 KB (13,017 words) - 20:26, 23 February 2019
• Cubical calculus
  <center> ''a function on the right and its derivative is on the left''. </center> ...fferential forms. Then the form on the left is what we call the ''exterior derivative'' of the form on the right. Consequently, the theorem can be turned into a
  25 KB (4,238 words) - 02:30, 6 April 2016
• Functions of several variables: derivatives and integrals
  ==The derivative of a function of several variables== First let's look at the point-slope form of ''linear functions'':
  42 KB (6,904 words) - 15:15, 30 October 2017
• Functions of several variables
  ...lumn of this table. It is now time to move to the right. We retreat to the first cell because the new material does not depend on the material of Chapter 17 ...numerical functions. Hence the need for parametric curves. Similarly, the first cell of the second column has surfaces but not all of them because some of
  97 KB (17,654 words) - 13:59, 24 November 2018
• Tangent bundles
  ...arer when the dimension of the space is $2$ or higher. We use ''vectors''. First, as we just saw, the work of the force is $W = \pm F \cdot D$ if $F || D$, First, what is the set of all possible directions on a ''graph''? We've come to u
  16 KB (2,753 words) - 13:55, 16 March 2016
• Calculus of sequences
  First, imagine that our speedometer is broken. What do we do if we want to estima *after the first hour: $10,055$ miles;
  113 KB (18,425 words) - 13:42, 8 February 2019
• Derivative as a function
  ==Motion and the derivative== ...have three values of $g^{\prime}$. That a new function! It is called the ''derivative function''.
  9 KB (1,437 words) - 14:05, 7 October 2012
• Calculus exercises: part III
  Solution: The first two components indicate that for Solution: The first component is defined and continuous for
  46 KB (8,035 words) - 13:50, 15 March 2018
• Vector and complex variables
  .... Solve the new equation: $-x=-4$, or $x=4$. Substitute this back into the first equation: $(4)+y=6$, then $y=2$. The four coefficients of $x,y$ form the first table:
  113 KB (18,750 words) - 02:33, 10 December 2018
• Transformations
  .... Solve the new equation: $-x=-4$, or $x=4$. Substitute this back into the first equation: $(4)+y=6$, then $y=2$. Let's collect the data in tables first:
  46 KB (7,625 words) - 13:08, 26 February 2018
• Applications of ODEs
  *first, the one with the sides $p_n-x_n$ and $y_n-q_n$, and First, the characteristic polynomial is:
  50 KB (8,692 words) - 14:29, 24 November 2018
• Combinatorial cell maps
  ...result is used as a template to define cell maps. The difference is that, first, if $f(s)$ is attached to itself along its boundary but $s$ isn't, cloning ...h of these examples, an idea of a map $f$ of the circle/square was present first, then $f$ was realized as a chain map $g$.
  31 KB (5,330 words) - 22:14, 14 March 2016
• Differential equations
  Recall first that an ''augmented partition'' of an interval $[a,b]$ is a sequence of $n$ In the meantime, the derivative, if any, would satisfy the following:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Extrema of functions of several variables
  *solve [[derivative|$f'(x)$]] $= 0$ for $x$, (also find $x$'s for which $f'(x)$ does not exist) *[[second derivative test]]: classify the critical points based on the sign of $f' '(a)$. Note t
  9 KB (1,511 words) - 16:07, 17 August 2011
• PDEs
  ...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 *$d_t$ is the exterior derivative with respect to time (just the difference in ${\mathbb R}$); and
  44 KB (7,469 words) - 18:12, 30 November 2015
• Functions of several variables OLD
  First, we have replaces the absolute value with the [[norm]]. This simply reflect To define [[derivative]]s we need limits and for [[limits]] we need to understand better the [[top
  34 KB (5,636 words) - 23:52, 7 October 2017
• Vector fields
  The first metaphor for a vector field is a ''hydraulic system''. *$m$ is the mass of the first object;
  91 KB (16,253 words) - 04:52, 9 January 2019
• 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
• Diffusion equation
  ...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 *$d_t$ is the exterior derivative with respect to time (simply the difference in ${\mathbb R}$); and
  35 KB (5,917 words) - 12:51, 30 June 2016
• Systems of ODEs
  First, we assume that they have an unlimited food supply and reproduce in a manne First, we assume that the foxes have only a limited food supply, i.e., the rabbit
  63 KB (10,958 words) - 14:27, 24 November 2018

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