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• Isotropy in numerical PDEs
  '''[[Heat equation]]''' '''[[Wave equation]]'''
  10 KB (1,593 words) - 13:20, 8 April 2013
• Freshman's introduction to discrete calculus
  ==The differential== '''Definition.''' The ''differential of a node function'' $f$ at edge $[A,B]$ is defined to be the number
  42 KB (7,443 words) - 14:18, 1 August 2016
• Modelling with discrete vector fields and forms
  ...escribe motion in dimension $1$. It is given by an [[ordinary differential equation]] (ODE): ...continuous and $x:I \to R$ is differentiable on an open interval $I$. The equation has to be satisfied for all $t \in I$.
  9 KB (1,561 words) - 16:06, 27 August 2015
• Navier–Stokes equations
  These are [[partial differential equations]] that describe the motion of fluid. ==Switch to differential forms==
  5 KB (742 words) - 03:32, 30 August 2012
• Peter Saveliev's Academic Portfolio
  *MTH 335 [[Differential Equations -- Fall 2011]] .../Teaching/Fall10/m691/syllabus.html Differential geometry] (new course), [[differential forms: course#Lectures|TeX lecture notes]]
  25 KB (3,536 words) - 14:28, 17 January 2017
• Elementary PDEs
  ...s, $d_x$, to be taken into account. The result is a ''partial differential equation'' (PDE). The result of the substitution is a PDE of second degree called the ''heat equation'' of cochains:
  16 KB (2,843 words) - 21:41, 23 March 2016
• Elementary ODEs
  We start with ''ordinary differential equations (ODEs) of cochains'' with respect to their exterior derivative $d This equation has a solution, i.e., a $0$-cochain that satisfies the equation for every $1$-cochain $a$:
  16 KB (2,913 words) - 22:40, 15 July 2016
• Maxwell equations
  ...n of the equations. Maxwell equations have long been written in terms of [[differential forms]] so I just need to interpret them as discrete ones, in order to deri The "differential forms" of the equations, i.e., the [[PDEs]]:
  6 KB (922 words) - 00:30, 9 April 2016
• Discrete calculus article
  ...alculus has two entry points, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of piece-wise Discrete differential calculus is the study of the definition, properties, and applications of th
  27 KB (4,329 words) - 16:02, 1 September 2019
• Differential equations: midterm
  These are exercises for [[Differential equations: course]] #Solve the differential equation: $y^{\prime}=-6xy.$
  1 KB (173 words) - 19:03, 1 November 2011
• Applications of ODEs
  We derive from the last equation the following: Solving this equation for $\Delta p_n$, we choose the negative sign for the square root:
  50 KB (8,692 words) - 14:29, 24 November 2018
• Computational science training: 2012
  *[[Differential equations: course]], just the basic ideas; *[[Differential forms: course]], at least the discrete part.
  5 KB (732 words) - 17:42, 8 April 2013
• Systems of ODEs
  We solve the equation: We solve the equation:
  63 KB (10,958 words) - 14:27, 24 November 2018
• Advanced Topology: exercises
  #Show that the set of differential forms is a vector space. #Form the axiomatic definition of differential form, prove that $\Omega^1(p)=span\{dx,dy\}.$
  9 KB (1,487 words) - 18:18, 9 May 2013
• Wave equation from Maxwell equations
  The "differential forms" of the [[Maxwell equations]]: ==Maxwell equations of differential forms==
  4 KB (655 words) - 14:51, 13 July 2012
• Continuous vs discrete differential forms
  ...lization of a [[cubical complex]] $K$ (or [[cell complex]]) and [[discrete differential forms]], i.e., [[cochains]], over $K$. So far, we have observed only that t We have thought of continuous [[differential forms]], $\varphi \in \Omega ^k ({\bf R}^n)$, mainly as ''integrands''. Als
  9 KB (1,483 words) - 13:54, 13 April 2013
• Discrete differential geometry
  .... We follow a broad approach to these issues by developing, in addition to differential calculus, its discrete version as well as other possible calculi. We borrow *Calculus of [[discrete differential forms]]
  3 KB (361 words) - 14:41, 19 July 2013
• Current students' projects
  *What parts of calculus, ODEs, PDEs, differential geometry, etc have discrete counterparts? ...ysics, represent each quantity as a [[discrete differential forms|discrete differential form]] of appropriate degree determined by its nature. These equations are
  4 KB (527 words) - 14:04, 25 August 2013
• Parametric curves
  Recall some motivation for differential calculus, from Calc 1. ...where $f$ is the location. Then $|| f ||^2$ = constant, differentiate the equation. $( (|| f ||)^2 )′ = 0$, so $2< f', f' > = 0$, thus $< f', f > = 0$. Henc
  34 KB (5,665 words) - 15:12, 13 November 2012
• Modern Thermodynamics by John Denker
  The terminology is different sometimes... "The term “inexact differential” is sometimes used in this connection, but that term is a misnomer, or at I agree that "differential" is out of place. "Inexact" might be an idiom but with a meaningful mathema
  8 KB (1,251 words) - 03:54, 29 March 2011

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