Learning derivations versus solving problems

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In summary, understanding the derivation of formulas is important in physics as it helps to understand the underlying principles and constraints that are used to solve problems and apply them in real world situations. It is also important to internalize the steps used in deriving formulas in order to effectively solve problems and avoid mistakes.
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spaghetti3451
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Hi, I understand when I study a physics topic, it's very important that I solve as many problems as I can possibly can and it's also very important to internalise all the techniques used to solve problems in that topic.

However, I was wondering if the same applies for the derivation of formulae that precedes the exercises in textbooks. I know that it's good to understand the derivation of the different formulae, but would you say that I would also have to internalise the steps used to derive the formulae.

For example, I'd be able to solve time-independent pertubation problems without any mistakes if you wake me up at four o'clock in the morning, but in deriving the corrections to the pertubed eigenvalues and eigenfunctions, I'd get stuck and make tonnes of mistakes along the way.
 
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Deriving the formula is a kind of boundary value problem ie the formulas come out of certain restrictions posed. It's really useful to understand this as it comes up in real world problems where you must decide what principles to use and what constraints are present.
 

1. What is the difference between learning derivations and solving problems?

Learning derivations involves understanding the underlying principles and concepts behind a mathematical formula or theorem, while solving problems simply requires applying those formulas or theorems to specific scenarios or equations.

2. Which approach is more effective for understanding complex mathematical concepts?

Many experts believe that learning derivations is a more effective approach for understanding complex mathematical concepts. By understanding the theory behind a formula or theorem, it becomes easier to apply it to various problems and scenarios.

3. How can learning derivations benefit problem-solving skills?

Learning derivations can help improve problem-solving skills by providing a deeper understanding of mathematical concepts. This can make it easier to identify the appropriate formulas or theorems to use in a given problem and apply them correctly.

4. Is one approach better than the other for all types of mathematical problems?

It ultimately depends on the individual and the specific problem. Some people may find it easier to learn derivations for certain types of problems, while others may prefer to simply solve problems using established formulas and theorems. Both approaches have their benefits and it may be helpful to use a combination of both.

5. Is it necessary to learn derivations if I just want to solve practical problems?

It is not necessary to learn derivations if your goal is solely to solve practical problems. However, learning derivations can provide a deeper understanding of mathematical concepts, which may ultimately make it easier to solve problems and apply formulas in real-world scenarios.

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