MadSci Network: Physics
Query:

Re: differential equations and physics

Date: Mon Oct 13 09:52:32 2003
Posted By: Dan Berger, Faculty Chemistry/Science, Bluffton College
Area of science: Physics
ID: 1065829863.Ph
Message:

Why are the fundamental laws of physics cast in the form of differntial equations, not algebraic equations?
Because physics likes to describe changes in properties as functions of other properties or things. This sort of relationship is best described by a differential equation.

Once a differential equation is integrated, it becomes an algebraic equation; so one could say that most or all of the fundamental laws of physics can also be stated in simple algebraic form. For example, consider the relationship between position, velocity and acceleration.

  1. Velocity is the rate at which position changes with time, dx/dt. If we integrate, we get the familiar equation x = vt.
  2. Acceleration is the rate at which velocity changes with time, dv/dt or d(dx/dt)/dt which can be stated as d2x/dt2. Integrated, we get the familiar algebraic form, x = 0.5 at2, or more generally
    x = x0 + v0t + 0.5 at2.
Changes in the pressure or volume of a gas with temperature can also be related by differential equations, such as dV/dT = nR/P for change in volume with temperature at constant pressure.

But only relationships in which one thing changes with respect to another are stated in terms of differential equations. For example, consider the formula for the energy of a photon, e = hn. The energy e and frequency n of a photon are related by Planck's constant h and do not change.

Dan Berger
Bluffton College
http://www.bluffton.edu/~bergerd



Current Queue | Current Queue for Physics | Physics archives

Try the links in the MadSci Library for more information on Physics.



MadSci Home | Information | Search | Random Knowledge Generator | MadSci Archives | Mad Library | MAD Labs | MAD FAQs | Ask a ? | Join Us! | Help Support MadSci


MadSci Network, webadmin@www.madsci.org
© 1995-2003. All rights reserved.