Approaching physics mathematically-help

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Studying physics requires a balance between intuitive understanding and mathematical application. While intuitive problem-solving can lead to correct answers, it may also result in incomplete analysis and potential errors. To improve mathematical skills in physics, consistent practice is essential. Start by clearly writing out assumptions, drawing diagrams, and formulating basic equations for each problem. If stuck, describe the problem in detail to clarify your thoughts. If a problem remains unsolved after an hour, consider moving on and revisiting it later. This systematic approach can enhance understanding and problem-solving abilities. While some may find it easier to integrate math into physics, it's important to develop both intuitive and analytical skills for a comprehensive grasp of the subject.
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Hey I've been studying physics for a while and recently I am taking AP physics and I am good at tackling physics intuitively, however when it comes to describing problems in equations I seem sometimes to have some trouble even although my mathematical skills are pretty good. I just need some advice on how to get better at using my mathematical skills throughout physics without having a problem doing so (and also tell me if there are any books that would help me tackle this problem).That is all and thank you.
 
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Tackling problems intuitively can mean that you're not taking the time to fully reason out the answer. If you read a problem, come up with an answer that seems obvious and more often than not you're consistent with the correct answer - this doesn't mean you're doing a complete job of analysing the problem and will pave the way for errors down the road.

Of course, you're asking how to correct this. And the answer is simple: practice. Even for problems that seem to have an intuitive answer, start by writing everything out.
 
Welcome to the party. This is the whole point of the college education process. It takes a lot of practice to become good at what you're talking about. I don't really have any specific suggestions, just keeping working problems and you'll improve with time. It gets easier.

One thing you can do is try to be systematic. Start out writing your assumptions, draw a picture of the problem, and then maybe write some basic equations. If you become stuck, it is often helpful to try and think through the problem and write out a paragraph describing what is going on. If you still can't find a solution, you might have to try and be more clever or think of an alternative method. If you can't solve a problem in the first hour, then skip it, and go back to it later. That's all I can really say.
 
I am somewhat opposite to you, I find it easy to incorporate the math. Only difference is, my teacher says i should forget about the math and think more intuitively. I think this is a bad idea though so I will only take it for what its worth.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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