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• Differential calculus of parametric curves
  '''Example (Newton's Law of Gravity).''' We have already seen examples of some of these behaviors ex Second, let's suppose that $X$ is continuous at this $t=s$. Then,
  130 KB (22,842 words) - 13:52, 24 November 2018
• Applications of ODEs
  *second, the one with the sides $-\Delta p_n$ and $\Delta q_n$. *$s=30$ feet per second;
  50 KB (8,692 words) - 14:29, 24 November 2018
• Applications of differential calculus
  ==Solving equations numerically: bisection and Newton's method== [[image:Newton's method.png| center]]
  59 KB (10,063 words) - 04:59, 21 February 2019
• Calculus I, the discrete version
  The second idea is illustrated below: Second, we assume that the node function is followed by another function that is s
  64 KB (11,521 words) - 19:48, 22 June 2017
• Freshman's introduction to discrete calculus
  ==Concavity and the second derivative== '''Definition.''' Given a node function its ''second derivative'' is the derivative of its derivative:
  42 KB (7,443 words) - 14:18, 1 August 2016
• Introduction to discrete calculus
  ...d $s$, as a function, from single edges to their combinations, $1$-chains. Second, we need ''additivity'' of $s$ as a function: ...hat there is no derivative of a $1$-chain precludes the possibility of the second exterior derivative to have any meaning. Instead, we utilize the dual struc
  40 KB (6,983 words) - 19:24, 23 July 2016
• Functions in higher dimensions
  The second requirement is called the ''right-hand rule''. Indeed, if we curl our finge ...moreover, for the distance to be zero, the two points have to be the same. Second, the distance from $P$ to $Q$ is the same as the distance from $Q$ to $P$.
  113 KB (19,680 words) - 00:08, 23 February 2019
• Calculus of chain maps
  Second, we need to understand what will happen to the edge $AB$. The only option i The second possibility is:
  41 KB (7,344 words) - 12:52, 25 July 2016
• Partial differential equations
  The process we are to study obeys the following familiar law of physics. '''Newton's Law of Cooling:''' <!--\index{Newton's Law of Cooling}--> The rate of cooling of an object is proportional to the diff
  53 KB (9,682 words) - 23:19, 18 November 2018
• Functions of several variables
  ...ns. Hence the need for parametric curves. Similarly, the first cell of the second column has surfaces but not all of them because some of them fail the verti Second, we fix $x$ and change $y$. We make a step along the $y$-axis with the $y$-
  97 KB (17,654 words) - 13:59, 24 November 2018
• Vector fields
  The second metaphor for a vector field is a ''flow-through''. '''Example (gravity).''' Recall from Chapter 21 that ''Newton's Law of Gravity'' states that the force of gravity between two objects is given
  91 KB (16,253 words) - 04:52, 9 January 2019
• Topology Illustrated -- Index
  *[[Law of Conservation of Momentum|Law of Conservation of Momentum]] *[[Newton's First Law|Newton's First Law]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Metric tensor
  ...oint where we start to need geometry is when we move from the first to the second derivative. ...rate of change of the rate of change. But, with $dd=0$, we don't have the second ''exterior'' derivative!
  42 KB (7,131 words) - 17:31, 30 November 2015
• Differential equations
  '''Example (Newton's Law of Cooling).''' Description: “the rate of cooling is proportional to the The formula was used in Chapter 10 to model Newton's Law of Cooling:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Geometry
  ...oint where we start to need geometry is when we move from the first to the second derivative. ...rate of change of the rate of change. But, with $dd=0$, we don't have the second ''exterior'' derivative!
  41 KB (6,928 words) - 17:31, 26 October 2015
• Diffusion equation
  The process we are to study obeys the following law of physics. '''Newton's Law of Cooling:''' <!--\index{Newton's Law of Cooling}--> The rate of cooling of an object is proportional to the diff
  35 KB (5,917 words) - 12:51, 30 June 2016
• Calculus of sequences
  *after the second hour: $10,095$ miles; *distance covered during the second hour: $10,095-10,055=40$ miles;
  113 KB (18,425 words) - 13:42, 8 February 2019
• Functions of several variables: derivatives and integrals
  What is the meaning of the composition in the second part of the Chain Rule? ...ion: From the first equation, we derive: $y=6-x$. Then substitute into the second equation: $2x+3(6-x)=14$. Solve the new equation: $-x=-4$, or $x=4$. Substi
  42 KB (6,904 words) - 15:15, 30 October 2017
• Limits and continuity
  The second is the ''fractional part'': ...n right. The interpretation of the result is possible if we understand the law correctly. The tax rate is ''marginal'', i.e., it is the tax rate applied t
  107 KB (18,743 words) - 17:00, 10 February 2019
• PDEs
  The process we are to follow is the ''Newton's Law of Cooling'': This law is nothing but a version of the ODE of population growth and decay -- with
  44 KB (7,469 words) - 18:12, 30 November 2015
• Modeling with discrete exterior calculus
  ==Newton's Law of Cooling== ...e inspected a simpler idea. In a 0-dimensional continuous form, [[Newton's Law of Cooling]] is \begin{equation} \frac{d T}{d t} = -k(T-S) \end{equation}
  31 KB (5,254 words) - 17:57, 21 July 2012
• Diffusion
  ...he four adjacent rooms. Moreover, the process has to follow the ''Newton's Law of Cooling'': the rate of cooling of an object is proportional to the diffe '''Notation.''' Below we routinely suppress $t$ as the second variable.
  39 KB (6,850 words) - 15:29, 17 July 2015
• Applications of integral calculus
  The second approach is to think of each location with higher velocity as simply one wi ...gned) distance of the object to its equilibrium according to the ''Hooke's Law'':
  103 KB (18,460 words) - 01:01, 13 February 2019
• Elementary PDEs
  The process we are to study obeys the following law of physics. '''Newton's Law of Cooling:''' <!--\index{Newton's Law of Cooling}--> The rate of cooling of an object is proportional to the diff
  16 KB (2,843 words) - 21:41, 23 March 2016
• Calculus exercises: part I
  *(a) Analyze the first and second derivatives of the function $f(x)=x^4-2x^2$. (b) Use part (a) to sketch its ...of the chocolate after another hour. (2) Provide the formula for Newton's Law of Cooling and explain.
  49 KB (8,436 words) - 17:14, 8 March 2018
• ODEs
  Second, since complex $K$ has no algebra that we use, This is a second order ODE with respect to $r$. Its initial values problem (IVP) includes bo
  47 KB (8,415 words) - 15:46, 1 December 2015
• Calculus exercises: part IV
  #$y'=y^2$ is a second order ODE. $\bullet$ According to Newton's law of cooling, the change of the temperature $T$ of a body immersed in a mediu
  13 KB (2,128 words) - 02:28, 5 September 2017
• Discrete calculus article
  ...s a [[linear operator]] which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes st ...cceleration is the difference quotient of velocity with respect to time or second difference quotient of the spatial position. Starting from knowing how an o
  27 KB (4,329 words) - 16:02, 1 September 2019
• Integrals of functions of several variables
  Second, we have a partition of $[c,d]$ into $m$ intervals of possibly different le Our analysis amounts to the following formula similar to the formula for the second, mixed partial derivative.
  73 KB (13,324 words) - 14:06, 24 November 2018
• Elementary ODEs
  This is a second order ODE with respect to $r$. Its initial value problem (IVP) includes bot The equation of the motion is derived from Hooke's law: the force exerted on the object by the spring is proportional to the displ
  16 KB (2,913 words) - 22:40, 15 July 2016
• Wave equation
  According to Hooke's law, the force exerted by the spring is Note that for a constant $k$, we are dealing with the second derivative of the $0$-form $u$ with respect to space:
  10 KB (1,775 words) - 02:40, 9 April 2016
• Topology
  The second question may be: this porous material is supposed to stop a flow of liquid; ...patterns'' in data. So, is there a pattern in this point cloud and maybe a law of nature that has produced it? What shape is hinted by the data?
  20 KB (3,407 words) - 21:46, 30 November 2015
• Calculus I -- Fall 2017
  ...ulation to test the objective from an Excel and MicrostationV8i. Using the law of reflection and tangencies to accompany my findings, could it have been t ...s and intervals of increase and decrease. Concavity and inflection points. Newton's Method. Differentials and linear approximation. Applications of derivatives
  13 KB (2,075 words) - 13:35, 27 November 2017
• College Algebra -- Fall 2014
  *week 2, 9/1: ''Second HW called Sections1.1-1.2 is due Friday 9/5 at midnight.'' Quiz 6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
  6 KB (850 words) - 16:52, 29 November 2014
• College Algebra -- Fall 2013
  *week 2, 9/5: '''Second HW called Sections1.1-1.2 is due Wednesday 9/11 at midnight.''' 6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
  6 KB (752 words) - 04:19, 13 December 2013