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• Price dynamics
  *Rescaling should affect the dynamics in a continuous fashion. *Rescaling shouldn't affect the direction of the dynamics at all.
  38 KB (2,588 words) - 14:23, 19 September 2012

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• ODEs
  The actual dynamics resembles that of your bank account: once a year the current amount is chec '''Exercise.''' Confirm that the dynamics is as expected for all values of $k>0$ and $k<0$.
  47 KB (8,415 words) - 15:46, 1 December 2015
• Continuous functions
  ...unction $x:I\to S$ of time $t$, where $I$ is some interval. Meanwhile, the dynamics of the particle is governed by the velocity of the flow, at each location a Let's start with dimension $1$ and $S:={\bf R}$. Then this dynamics is given by an ''ordinary differential equation'' (ODE):
  42 KB (7,138 words) - 19:08, 28 November 2015
• Euler and Lefschetz numbers
  ...Is it possible for them to stay constant? In other words, does every price dynamics allow an equilibrium? The dynamics of prices is captured by a continuous function $F:P\to P$. However, we know
  41 KB (7,169 words) - 14:00, 1 December 2015
• Systems of ODEs
  Let's take a look at an example of a possible dynamics ($\alpha=0.10$, $\beta=0.50$, $\gamma=0.20$, $\delta=0.20$, $h=0.2$): We will investigate the dynamics at all locations in the first quadrant of the $tx$-plane.
  63 KB (10,958 words) - 14:27, 24 November 2018
• Price dynamics
  *Rescaling should affect the dynamics in a continuous fashion. *Rescaling shouldn't affect the direction of the dynamics at all.
  38 KB (2,588 words) - 14:23, 19 September 2012
• More ODEs
  ...is a function $u:{\bf Z}^+\to {\bf R}^2$ of time $t\ge 0$. Meanwhile, the dynamics of the particle is governed by the velocity of the flow, at each moment of ...ets<!--\index{spreadsheet}-->, such as Excel, can be used to model various dynamics and some of the processes can also be visualized.
  26 KB (4,649 words) - 12:43, 7 April 2016
• Elementary ODEs
  The actual dynamics resembles that of a bank account: once a year the current amount is checked '''Exercise.''' Confirm that the dynamics is as expected for all values of $k>0$ and $k<0$.
  16 KB (2,913 words) - 22:40, 15 July 2016
• Computational Homology by Kaczynski, Mischaikow, Mrozek
  **1.2 Nonlinear Dynamics *10 Nonlinear Dynamics
  5 KB (616 words) - 14:03, 6 October 2016
• Applications of ODEs
  Imagine a hound running after a rabbit. Let's investigate their mutual dynamics. ...r 21 we used the discrete equation above to the motion of spring and other dynamics. What about the other equation? In the simplest case $a=0$, it was also sol
  50 KB (8,692 words) - 14:29, 24 November 2018
• Cluster size effects in molecular beam scattering
  ''Adsorption Dynamics of CO on Silica Supported Gold Clusters: Cluster Size Effects in Molecular ...e gold metal clusters on gas-surface energy transfer processes (adsorption dynamics)... For the statistical analysis, commercial imaging analysis software (Pix
  1 KB (132 words) - 15:10, 9 October 2010
• Applications of differential calculus
  ...idered an example of how functions appear as direct representations of the dynamics given by an indirect description: motion's velocity is derived from the acc Suppose we know the forces affecting a moving object. How can we predict its dynamics?
  59 KB (10,063 words) - 04:59, 21 February 2019
• Calculus of sequences
  '''Example (Newton's Law of Cooling).''' The dynamics of cooling of an object is depends on the difference between its temperatur Such a sequence is called a ''logistic sequence''. Its dynamics dramatically depends on $r$:
  113 KB (18,425 words) - 13:42, 8 February 2019
• Several variables
  ...vertical and horizontal directions, simultaneously and independently. The dynamics is very different. In the ''horizontal'' direction, as there is no force ch Any possible dynamics is found by specifying the values of the four constants:
  76 KB (13,017 words) - 20:26, 23 February 2019
• Vector fields
  ...rplane in a wind-tunnel. A similar idea is used to model a fluid flow. The dynamics of each particle is governed by the velocity of the flow, at each location, Suppose we know the forces affecting a moving object. How can we predict its dynamics?
  91 KB (16,253 words) - 04:52, 9 January 2019
• Partial differential equations
  ...the distribution of heat throughout the rod at every moment of time or the dynamics of the temperature at every location. Conclusion: the temperature evens out ...xample, a square heater in the middle of a room will produce the following dynamics of distribution of the temperature over the floor:
  53 KB (9,682 words) - 23:19, 18 November 2018
• Lefschetz numbers in control theory
  ...tions of the Lefschetz fixed point theory techniques, already available in dynamics, in control theory. ...and input spaces, we can gain insight from this theorem into the possible dynamics of the system. For example, the condition of the theorem holds if $H_{2k}(N
  17 KB (3,052 words) - 22:12, 15 July 2014
• Elementary PDEs
  ...he general case of edges/rooms of arbitrary size. Then what determines the dynamics of the heat transfer isn't the amount of heat $U(a)$ in room $a$ but its '' The simplest way to implement this dynamics with a spreadsheet is to use the first two rows for the initial conditions
  16 KB (2,843 words) - 21:41, 23 March 2016
• Differential Equations -- Spring 2017
  *4a. How would predator and prey populations interact when their dynamics is affected by seasons? ([http://users.marshall.edu/~saveliev/Teaching/Spri *4b. How would predator and prey populations interact when their dynamics is affected by random fluctuation?
  9 KB (1,360 words) - 15:10, 1 June 2017
• Differential equations
  ...motion: if we know the ''velocity'' of a moving object, we can predict its dynamics. For example, the ODE: ...ecting the object and, therefore, its acceleration. How can we predict its dynamics?
  64 KB (11,426 words) - 14:21, 24 November 2018
• Calculus projects
  ...atement'': (a) How would predator and prey populations interact when their dynamics is affected by seasons? ([http://users.marshall.edu/~saveliev/Teaching/Spri ...atement'': (b) How would predator and prey populations interact when their dynamics is affected by random fluctuation?
  13 KB (2,078 words) - 22:43, 26 October 2019
• Publications that use Pixcavator
  ...s=SpellE>Burghaus</span>, <i style='mso-bidi-font-style:normal'>Adsorption dynamics of CO on silica supported gold clusters: cluster size effects in molecular
  17 KB (2,350 words) - 14:40, 4 November 2011
• Computational topology
  #Topological Dynamics: Rigorous Numerics via Cubical Homology by Marian Mrozek
  5 KB (748 words) - 19:24, 31 January 2015
• The derivative
  The dynamics is very different. In the horizontal direction, as there is no force changi
  75 KB (13,000 words) - 15:12, 7 December 2018
• Differential calculus
  We then derive the ''dynamics'' of this situation:
  84 KB (14,321 words) - 00:49, 7 December 2018
• What shape of sword is best for cutting?
  Now the guillotine. The dynamics is the same except its knife has a ''slope'' and the edge seems to be movin
  14 KB (2,504 words) - 14:59, 17 September 2019
• Differentiation
  ...its derivative are two animals of very different breeds. As a result, the dynamics discussed above will disappear in higher dimensions.
  82 KB (14,116 words) - 19:50, 6 December 2018
• Introduction to Topology: Pure and Applied by Adams and Franzosa
  ** 8.4. A Simple Population Model with Complicated Dynamics
  3 KB (311 words) - 13:36, 26 October 2012
• Applications of Lefschetz numbers in control theory by Saveliev
  ...ns the [[Lefschetz fixed point theory]] techniques, already available in [[dynamics]], in [[control theory]]. A [[dynamical system]] on a [[manifold]] $M$ is d
  2 KB (341 words) - 13:55, 26 March 2011
• Material derivative
  In [[fluid dynamics]], the velocity field is the flow velocity itself (i.e., a [[vector field]]
  2 KB (388 words) - 21:31, 17 July 2012
• Applied Differential Geometry by Burke
  *7. Dynamics of particles and fields;
  537 bytes (53 words) - 13:39, 5 October 2012
• Modelling with discrete vector fields and forms
  ...ourse, in the case of a IVDE both $x_n$ and $F$ are integer-valued and the dynamics is integer-valued too. As a result the complexity is diminished. In particu
  9 KB (1,561 words) - 16:06, 27 August 2015
• Applied algebraic topology
  **2.4.7 [[Continuous_functions#The_dynamics_of_a_market_economy|The dynamics of a market economy]]
  4 KB (545 words) - 13:18, 29 October 2015
• Navier–Stokes equations
  Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining
  5 KB (742 words) - 03:32, 30 August 2012
• CHomP
  ...gers University and [http://capd.ii.uj.edu.pl/ Computer Assisted Proofs in Dynamics group], Jagiellonian University, Krakow, Poland
  2 KB (255 words) - 16:13, 5 April 2011
• Excel simulations
  ...xample, a square heater in the middle of a room will produce the following dynamics of distribution of the temperature over the floor. [https://youtu.be/QHcKfp
  5 KB (822 words) - 00:38, 3 September 2018
• Calculus exercises: part I
  ...pose $t$ is time and $x$ is the price of bread. What can you say about its dynamics? Be as specific as possible.
  49 KB (8,436 words) - 17:14, 8 March 2018
• Fluid flow
  *[http://http.developer.nvidia.com/GPUGems/gpugems_ch38.html Fast Fluid Dynamics Simulation on the GPU]
  647 bytes (92 words) - 21:48, 15 August 2011
• Discrete calculus article
  ...n determining reaction rates and radioactive decay. In biology, population dynamics starts with reproduction and death rates to model population changes.
  27 KB (4,329 words) - 16:02, 1 September 2019
• Functions in higher dimensions
  '''Example (thrown ball).''' Let's review the dynamics of a thrown ball. A constant force causes the velocity to change linearly,
  113 KB (19,680 words) - 00:08, 23 February 2019
• PDEs
  The simplest way to implement the dynamics with the above formula in Excel is to use the first two rows for the initia
  44 KB (7,469 words) - 18:12, 30 November 2015
• Homology software
  ...gers University and [http://capd.ii.uj.edu.pl/ Computer Assisted Proofs in Dynamics group], Jagiellonian University, Krakow, Poland
  4 KB (648 words) - 03:16, 30 March 2011