Losing ability of solving problems.

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SUMMARY

The discussion centers on the phenomenon of losing problem-solving skills in mathematics, particularly in the context of Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) due to a lack of regular practice. A participant highlights their transition from academic exercises to research in turbulence modeling, where complex equations are often unsolvable by hand. They express concern over forgetting fundamental techniques despite a deeper understanding of the concepts. The consensus is that this skill loss is common, but re-learning is achievable through regular practice using undergraduate physics and mathematics resources.

PREREQUISITES
  • Understanding of Ordinary Differential Equations (ODE)
  • Familiarity with Partial Differential Equations (PDE)
  • Basic knowledge of turbulence modeling
  • Experience with mathematical problem-solving techniques
NEXT STEPS
  • Review undergraduate textbooks such as "Byron and Fuller" for mathematical methods
  • Practice problem-solving using "Griffiths E&M" for physics applications
  • Explore "Morin's Classical Mechanics" for classical mechanics problems
  • Establish a regular schedule for revisiting and practicing mathematical techniques
USEFUL FOR

Students, researchers, and professionals in mathematics and physics, particularly those involved in fields requiring problem-solving skills in ODE and PDE, will benefit from this discussion.

Bunsen
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Hi guys!

Well, when I was a B.Sc and/or a M.Sc student I used to solve lots of exercises from books in order to prepare myself for exams. I was really familiar with many methods for solving ODE and PDE by hand and I was comfortable by doing it.

But since 3 years I am only working in research and, since the equations involved in my field (turbulence modeling) are unsolvable by hand for the complex situations which I work on, I just stopped to really "solve" them and in the last years I have focussed in their interpretation and in the understanding of concepts. Because of that, now I feel I have lost/forgotten a lot of tools required for solving the simple cases by hand, even when I understand the equations much better than what I did 3 years ago.

Do you think this situation is normal? or I am doing something wrong?

Thanks a lot for your comments...
 
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Unfortunately yes, it's normal to lose your skills if you don't use them on a regular basis.

The good thing is that re-learning them isn't all that difficult if you were proficient once.
 
Twice a year, typically around holidays, I take a couple undergrad physics books off the shelf and a math methods book. For example:

Byron and Fuller, Griffiths E&M, and Morin's Classical Mechanics. Then I try to solve a bunch of problems over a few days cold. If I forget a technique I give myself a crash course. Every christmas, spring holiday, Thanksgiving, etc I try to do this. It's nostalgic and fun.
 

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