Should I expect myself to "know everything"?

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SUMMARY

The discussion centers on the expectation of mastering complex problems in mechanics and applied mathematics. Participants agree that it is normal to struggle with novel problems, even after grasping the fundamentals. They emphasize the importance of breaking down complex problems into manageable parts and acknowledge that some problems may require consulting solution manuals. Ultimately, it is established that one should not expect to know everything, as even experienced individuals face challenges with new problems.

PREREQUISITES
  • Understanding of basic mechanics principles
  • Familiarity with problem-solving techniques in applied mathematics
  • Experience in breaking down complex problems into simpler components
  • Knowledge of consulting academic resources, such as solution manuals
NEXT STEPS
  • Explore advanced problem-solving techniques in applied mathematics
  • Learn methods for effectively breaking down complex mechanics problems
  • Study common variations of mechanics problems to build confidence
  • Research strategies for independent problem-solving without reliance on solution manuals
USEFUL FOR

Students in mechanics and applied mathematics, educators seeking to guide learners, and anyone looking to improve their problem-solving skills in complex subjects.

WWCY
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I'm not sure how to put this into words but...here goes.

After going through chapters and chapters of introductory mechanics, I think I can say that I at least some of the basics down. However, when I introduce myself to extremely novel problems, I get stunned at their complexity and have to resort to asking professors and consulting their "solution manuals".

My question is:
Is this normal? Or should one be able to sweep aside novel problems with some degree of ease if one understands the fundamentals (i.e I'm far off from understanding the fundamental bits of mechanics).

I know it might be a silly line of inquiry but I'm hoping to get insight from the more experienced to set up realistic targets for my work.
 
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One of the most important techniques for solving "complex" problems is to make them less complex by breaking them down into parts. This is not always easy of course and it can be particularly challenging if you lack experience. No one knows "everthing" and some folks are better than others in figuring out how to get started on problems.

How about you give a specific example of a problem that you experienced this with so we get a feel for just where you are?
 
WWCY said:
Is this normal?
Yes, but see below.
WWCY said:
Or should one be able to sweep aside novel problems with some degree of ease if one understands the fundamentals (i.e I'm far off from understanding the fundamental bits of mechanics).
I think it depends on how "novel" these problems are. When they are variations on the problems that you have been practicing with in class or in the book, I think you should be able to do them without consulting solution manuals. When they are slightly more difficult, I still believe you should be able to do them on your own, but it may require more time and effort. This is fine.

Yet, I am convinced that it is almost always possible to think of a new problem, using only concepts that were discussed in the course, and such that even the lecturer may have a hard time providing a solution. At least in my field (applied mathematics) this is the case.

So, no, you should not expect yourself to know everything, in the sense that you defined it.
 

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