 My Math Forum Is this an ordinary diff eq or a partial diff eq?
 User Name Remember Me? Password

 Calculus Calculus Math Forum

 July 7th, 2013, 12:22 AM #1 Newbie   Joined: Jun 2008 Posts: 28 Thanks: 0 Is this an ordinary diff eq or a partial diff eq? What if we have a diff eq where the unknown function depends on one variable (let's say u) and also explicitly on time (t) i.e. the unknown function = x(u,t) Is time really another variable, making the diff eq a partial diff eq? I've heard this explicit dependence on t by x be called "non-autonomous." Not sure if these terms are mutually exclusive or not. What if u also depends on time? What if u does not depend on time? Thanks! July 7th, 2013, 06:36 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Is this an ordinary diff eq or a partial diff eq? Time is a variable if it's a variable. If, say, y is the temperature on a bar (with x the length along the bar), and y = f(x), then f'(x) is the temperature gradient along the bar and this a normal derivative. If, however, you consider how the bar is cooling over time, then y = f(x, t). f is now a function of two variables, so the derivative above becomes a partial derivative of f (wrt x). This describes the temperature along the bar at a given point in time. And, you have another partial derivative of f which is wrt t. This describes the change in temperature over time at a given point along the bar. July 8th, 2013, 10:01 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Is this an ordinary diff eq or a partial diff eq? I think what you are saying is that you know how y depends upon t and have a differential equation showing how it depends upon x. In that case, we would consider t a parameter and have an ordinary differential equation for y as a function of x. Tags diff, ordinary, partial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post arron1990 Calculus 10 August 14th, 2012 11:01 AM FreaKariDunk Calculus 24 March 3rd, 2012 12:22 PM jakeward123 Calculus 5 February 1st, 2012 11:22 AM vt1992s10 Calculus 1 January 6th, 2009 04:19 AM amaciose Calculus 5 October 12th, 2008 04:10 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      