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• Applications of ODEs
  In this chapter, we will often refer to systems of ODEs as ''vector ODEs'' or simply ODEs. *$(x,y)$ is the location of the rabbit, and
  50 KB (8,692 words) - 14:29, 24 November 2018
• Applications of differential calculus
  ...numbers $d_n$ such that $d_n\to c$. Then $d_n$ are the ''approximations'' of the unknown $d$. ...search for a solution of the equation $f(x)=0$. We constructed a sequence of nested intervals<!--\index{nested intervals}--> by cutting intervals in hal
  59 KB (10,063 words) - 04:59, 21 February 2019
• Partial differential equations
  ...ces as if they are separate compartments: the heat is contained in a ''row of rooms'' and each room exchanges the material with its ''two neighbors'' thr *$a=AB$ is one of the rooms;
  53 KB (9,682 words) - 23:19, 18 November 2018
• ODEs
  Suppose $R$ is our ring of coefficients. '''Exercise.''' Give an example of $G$ so that the ODE has no solution.
  47 KB (8,415 words) - 15:46, 1 December 2015
• Calculus I, the discrete version
  We start by dividing the $x$-axis into intervals of equal length $h>0$ starting from some location $Q$: Then the two types of pieces:
  64 KB (11,521 words) - 19:48, 22 June 2017
• Metric tensor
  ...troduce an arbitrary geometry into the (so far) purely topological setting of cell complexes. ...that only the way the cells are attached to each other affects the matrix of the exterior derivative:
  42 KB (7,131 words) - 17:31, 30 November 2015
• Introduction to discrete calculus
  We next examine the combined ''domain'' of these new functions. We are to make the usual domain of functions -- the reals ${\bf R}$ -- discrete. We divide this set into unit
  40 KB (6,983 words) - 19:24, 23 July 2016
• Calculus of chain maps
  Suppose we have two copies of the complex ${\mathbb R}$, ${\mathbb R}_x$ and ${\mathbb R}_y$, possibly re ...represent motion in space. They have to somehow respect the cell structure of ${\mathbb R}$. Let's recall how ''cell functions'' are introduced.
  41 KB (7,344 words) - 12:52, 25 July 2016
• Geometry
  ...troduce an arbitrary geometry into the (so far) purely topological setting of cell complexes. ...that only the way the cells are attached to each other affects the matrix of the exterior derivative:
  41 KB (6,928 words) - 17:31, 26 October 2015
• Freshman's introduction to discrete calculus
  ...${\bf R}$ into discrete pieces. To begin with, we divide it into intervals of equal length $h>0$: The result is two types of pieces:
  42 KB (7,443 words) - 14:18, 1 August 2016
• Test
  [[Image:Tunnels_in_foam.png|200px|right|Complex 3d topology of a piece of foam]] A sample of the ideas that the text follows -- in broad brushstrokes.
  16 KB (2,139 words) - 23:01, 9 February 2015
• Applied Topology and Geometry
  [[Image:Tunnels_in_foam.png|200px|right|Complex 3d topology of a piece of foam]] A sample of the ideas that the text follows -- in broad brushstrokes.
  16 KB (2,088 words) - 16:37, 29 November 2014
• Elementary PDEs
  ==The PDE of heat propagation== ...ure of each room changes by a proportion of the average of the temperature of the four adjacent rooms. Its spreadsheet simulation is seen in the two imag
  16 KB (2,843 words) - 21:41, 23 March 2016
• Modern Thermodynamics by John Denker
  *"The first law of thermodynamics states that energy obeys a local conservation law. *The second law of thermodynamics states that entropy obeys a local law of paraconservation."
  8 KB (1,251 words) - 03:54, 29 March 2011
• Zachary Ahlers
  *[http://inperc.com/files/REU/LGCA/LGCAvideos.zip Videos of simulations] (zipped large) ...that transmit heat, but what physical purposes do the 0-cells (the corners of the rooms) have?
  8 KB (1,315 words) - 15:20, 10 August 2012
• Current students' projects
  *What parts of calculus, ODEs, PDEs, differential geometry, etc have discrete counterparts Is this of interest to the research community?
  4 KB (527 words) - 14:04, 25 August 2013
• Computational science training: 2012
  ...flat and curved “surface worlds” check the Euclidean theorem about the sum of the angles in a triangle. From G. Gamow, One, Two, Three... Infinity.]] ...try at Marshall University will jointly host twelve students for ten weeks of instruction and research in computational science.
  5 KB (732 words) - 17:42, 8 April 2013
• Discrete differential geometry
  ...''exactly'' rather than approximately, as is the case with discretization of PDEs. The next main issue is that, even if the discrete PDE is physically v *[[The algebra of chains]]
  3 KB (361 words) - 14:41, 19 July 2013
• Darcy's flow
  *$\mu$ is the viscosity of the fluid. For the single fluid phase, the [[conservation of mass]] produces the [[steady state]] equation called the '''pressure equation'''
  2 KB (343 words) - 12:45, 30 August 2013