RE: silly newbie questions
- To: mathgroup at smc.vnet.net
- Subject: [mg34403] RE: [mg34385] silly newbie questions
- From: "Curt Fischer" <cfisher at bio.titech.ac.jp>
- Date: Sat, 18 May 2002 03:51:09 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear Tom: >-----Original Message----- >From: theiman [mailto:heimantj at celera.com] To: mathgroup at smc.vnet.net >Sent: Friday, May 17, 2002 19:31 >Subject: [mg34403] [mg34385] silly newbie questions > >Hi, > >I have two questions: > >(1) I have an equation: > > eqn = A'[t] = S - (ln(2)/hl)*A[t] > >and I am trying to find the time at which the discontinuity >occurs (t1 >and t2) and I have sampled at time t. The constraints for the >system >are: > > S(t)=S if t1<t<t2 > S(t)=0 otherwise > >The question is: How do I use these constraints with Dsolve? ---------------------------- This should get you started: In[1]:= <<Calculus`DiracDelta` In[2]:= s[t_]:=ss (UnitStep[t-t1]-UnitStep[t-t2]) In[3]:= eqn=a'[t]==s[t]-Log[2/h1] a[t] Out[3]=<stuff> In[4]:= DSolve[{eqn,a[0]=a0},a[t],t] Out[4]=<stuff> The first line loads the package that lets you use the UnitStep fuction. This is one way to represent piecewise functions in Mathematica. The second line defines s[t] as a function of t--which is important because in a later DSolve statement we will want to preserve that functional dependence. The third line is your equation. Note the double equals "==" to represent a test for equality as opposed to the assignment operator "=" the single equals. The fourth line calls DSolve and generates a solution for a[t] in terms of t1 and t2, ss, and h1. I also included an initial condition. It sounds like at this point you will want to fit the function Mathematica gives you in Out[4] to your sampled data for t? Check the help browser for the built-in function Fit[ ] or for the add-on package Statistics`NonlinearFit`. If you want to use Laplace transforms look in the help browser under Calculus`LaplaceTransform`. Hope that helps. Regards, Curt Fischer Tokyo Institute of Technology Dept. of Bioengineering > >(2) After I find the solution to the equation in question 1 I >would >like to take the laplace transform of the equation (and since it >is a >step function I need to use the heaviside (formula/equation?)) >and >solve the result. Any ideas on how to do this? > >I would really appreciate any help or suggestions!!!! > >Thankyou!! > >Sincerely, > >Tom >