Advice Wanted:How To Solve A Problem Without Really Understanding It

  • Thread starter terryphi
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In summary, the speaker is seeking help with solving a problem involving an isotropic point source in a vacuum. They mention not having a background in tensor calculus but still wanting to solve the problem properly without just plugging values into a formula. They compare this to using differential calculus in physics and emphasize the importance of using a reliable mathematical model for the specific problem.
  • #1
terryphi
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Hi,

I'm in a situation where I know the formula I need to solve a problem but I don't know how to derive it.

(I'm trying to derive a formula for an isotropic point source in a vacuum)

The correct solution requires the use of Gauss's Theorem of Divergence, but I've never taken a course on tensor calculus.

Although it's a bit unorthodox, I'd still like to ask:

How can I solve this problem 'properly' (IE not just plugging values into a formulae) without going through a whole course on tensor calculus?

Or more generally:

How does one solve a problem without having the background?

Thanks for any insight you might have.
 
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  • #2
terryphi said:
How can I solve this problem 'properly' (IE not just plugging values into a formulae)

Maybe the following comparison is helpful. When a physicist uses differential calculas there is no obligation to derive differential calculus itself.

'Plugging values in a formula' is OK if that formula is in itself not specific to the problem at hand.

The obligation then is to give sound arguments that the mathematics of the particular formula you're using is a good model for the physics that you want to describe.
 

1. How can I solve a problem without really understanding it?

Solving a problem without understanding it may seem like a daunting task, but there are a few strategies you can use to approach it. First, try breaking the problem down into smaller, more manageable parts. This will help you focus on one aspect at a time and make it easier to understand. Additionally, you can try looking for patterns or similarities in the problem that may give you clues on how to solve it. Finally, don't be afraid to ask for help or advice from others who may have a different perspective on the problem.

2. Is it possible to solve a problem without understanding it completely?

Yes, it is possible to solve a problem without fully understanding it. This is because problem-solving often involves trial and error, and even if you do not fully understand the problem at first, you can learn and adapt as you go. It's important to keep an open mind and be willing to try different approaches until you find a solution that works.

3. What should I do if I'm struggling to understand a problem?

If you're having difficulty understanding a problem, take a step back and try to approach it from a different angle. This could mean taking a break and coming back to it later, or seeking help from someone else. It's also helpful to ask questions and clarify any confusing aspects of the problem. Don't get discouraged and keep an open mind – sometimes, a new perspective can make all the difference.

4. How important is it to fully understand a problem before trying to solve it?

While it's ideal to have a thorough understanding of a problem before attempting to solve it, it's not always necessary. As mentioned earlier, problem-solving often involves trial and error, and you can learn and adapt as you go. However, having a good understanding of the problem can make the process smoother and more efficient.

5. Can I use the same problem-solving approach for every problem?

No, different problems may require different problem-solving approaches. It's important to be flexible and adapt your strategy based on the specific problem at hand. Some problems may be more logical and require a step-by-step approach, while others may require a more creative or intuitive approach. It's important to be open to trying different strategies and finding what works best for each individual problem.

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