Perhaps some of my blog posts from the 2009 summer could also be converted into documentation. I derive the general solution for several methods, including variation of parameters (see http://asmeurersympy.wordpress.com/2009/08/01/variation-of-parameters-and-more/ for example). They're actually a little light on actual examples from dsolve(), but they describe in great detail the mathematical derivation of the general solution to the methods (in this case, we have one of the few pages that treats variation of parameters in the general nth case, instead of just the second order case that is usually taught in ODE courses). Other good ones are my post on first order equations with homogeneous coefficients (http://asmeurersympy.wordpress.com/2009/05/31/first-order-differential-equations-with-homogeneous-coefficients/), which is the only place I know that actually derives the general solutions in full to these equations, and the one on undetermined coefficients (http://asmeurersympy.wordpress.com/2009/08/17/undetermined-coefficients/).
Aaron Meurer 2011/9/14 Ondřej Čertík <[email protected]>: > On Wed, Sep 14, 2011 at 3:04 PM, David Joyner <[email protected]> wrote: >> On Wed, Sep 14, 2011 at 5:48 PM, Aaron Meurer <[email protected]> wrote: >>> What actually needs to be done? >> >> Well, basically just get a Sage trac account (I think just email >> sage-trac-account https://groups.google.com/group/sage-trac-account for >> that), >> click on the trac ticket and click positive review:-) To actually to the >> review >> correctly, see the appropriate sections of the developer's manual >> http://www.sagemath.org/doc/developer/ (for example I like >> http://www.sagemath.org/doc/developer/producing_patches.html >> to apply patches). >> >> >>> >>> On Wed, Sep 14, 2011 at 3:31 PM, David Joyner <[email protected]> wrote: >>>> Hi all: >>>> >>>> Just a little reminder: there is a trac item in Sage detailing with >>>> the upgrade of >>>> Sympy to 0.7.1 (from 0.6.4). I think almost anyone on this email list with >>>> sufficient interest could do this review: >>>> http://trac.sagemath.org/sage_trac/ticket/11560. >>>> It would be great if someone could find the time to do this. >>>> I have agree to write a review of a CAS for a December publication, >>>> and resolving this ticket would help a lot for examples I could give >>>> that mention Sympy. (I am thinking now it would possibly be on Sage >>>> but mention Sympy in some examples.) >>>> >>>> I'd also like to say that, thanks to the improvements to the >>>> Sympy 0.7.1 modules for dsolve (mostly due to Aaron Meurer), >>>> some DEs are solved by Sympy better than by Maxima - >>>> very useful for my day-to-day teaching! >>> >>> I wrote the initial ODE module, which was first included in 0.6.6, but >>> not much has changed since then. But I guess the most recent Sage >>> version is 0.6.4. Anyway, I haven't really done much work on it since >>> then :) >>> >>> I did notice at the time, though, that it was more powerful that >>> Maxima (or any other open source CAS that I knew of). For example, no >>> other open source system (or at least not Maxima) to my memory >>> bothered to implement the general nth order case for variation of >>> parameters. Also, I don't think things like first order ODEs with >>> homogeneous coefficients are implemented in Maxima, if I remember >>> correctly. >>> >>> Anyway, I'm glad to hear that it's been useful to you. >>> >>> By the way, do you find the hint manager useful for teaching? That >> >> >> Yes, it is. Sadly, it is not in Sage yet though... >> >> >>> was one of the motivations of implementing it, that it would be easy >>> to teach, e.g., the Bernoulli method and call dsolve(ode, f(x), >>> 'Bernoulli') or dsolve(ode, f(x), 'Bernoulli_Integral'), and it would >>> be very instructive, as the output would look exactly like it would if >>> you used that method by hand (especially the Integral output). >> >> >> Agreed. And, thanks very much for your hard work on improving >> this! > > David, is this the course that you are teaching from: > > http://www.usna.edu/Users/math/wdj/teach/sm212/ > > ? We should put some of the examples into sympy documentation, so far > we have this: > > http://docs.sympy.org/0.7.1/modules/solvers/ode.html > > but actually doing examples from an ODE course would be cool. For > example for the variation of parameters, I remember it was really > tedious to do by hand. It'd be cool to add couple more examples, > besides what we have here: > > http://docs.sympy.org/0.7.1/modules/solvers/ode.html#nth-linear-constant-coeff-variation-of-parameters > > Ondrej > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
