Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The algebraic manipulations for changing variables in PDE/ODE problems are often very simple once you know the transformation to use (at least at my level it's just applying the chain rule carefully). However, the geometric meaning of even a very simple non-linear transformation is often extremely difficult to visualise.

As I'm just starting out on a second course in PDE's (though the first was engineering-based) I thought it might be beneficial to ask for advice on what should be going through my mind when transforming a PDE. In particular, is there any way to 'understand' a transformation without relying on geometric intuition far better than my own. Currently I feel like a computer just using rules to transform an equation.


share|cite|improve this question
Maybe it would help if you gave an example of a simple-yet-difficult-to-visualize transformation. PDE is such a diverse subject that generic advice is not likely to be helpful. – user31373 Jul 27 '12 at 13:46
I'll second the notion that an example would be nice. One general principle, though, is that many useful transformations are associated with symmetries (of the space, the physical system, etc.). These can be subtle (as in soliton theory, say) and it can take a lot of experience, case by case, to develop deeper intuition. – Bob Pego Jul 27 '12 at 14:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.