Thread: Calculus and analysis in physics

Calculus and analysis are the base of modern mathematics. When we see maths in physics we find many demonstration using calculus but without the necessity rigoriste, for exemple in classical mechanics or analytic mechanics many demonstration using calculus without check limits or continuity of objects. They use tiny objects. I'm learning calculus and analytic mechanics however i'm starting to think mechanics and more widely physics aren't rigorous. I heard to speak about no-standard analysis but I don't know if it can say that physics are rigorous.

Originally Posted by Vision13

Calculus and analysis are the base of modern mathematics. When we see maths in physics we find many demonstration using calculus but without the necessity rigoriste, for exemple in classical mechanics or analytic mechanics many demonstration using calculus without check limits or continuity of objects. They use tiny objects.

Welcome to the forum!

That's not always so. When studying rigid body motion or oscillations that's certainly not true. And we study point objects because we have the superposition principle which allows us to build on that to study macroscopic bodies. I.e. when you're ready and have enough training and the subject material requires it then you can move on to textbooks on continuum mechanics. See, for example Continuum Mechanics and Plasticity (Modern Mechanics and Mathematics) at Continuum Mechanics and Plasticity (Modern Mechanics and Mathematics) | Han-Chin Wu | digital library BookOS

Originally Posted by Vision13

I'm learning calculus and analytic mechanics however i'm starting to think mechanics and more widely physics aren't rigorous.

That's certainly not true whatsoever! You just have a very long way to go before you can say that you know everything. Mechanics is a large subject and can't be learned in from one text in one course. I suspect thatr you haven't even gotten to the point where you've studied the math for that which requires tensor analysis. Is that correct?

Originally Posted by physicist

Originally Posted by Vision13

I'm learning calculus and analytic mechanics however i'm starting to think mechanics and more widely physics aren't rigorous.

That's certainly not true whatsoever! You just have a very long way to go before you can say that you know everything. Mechanics is a large subject and can't be learned in from one text in one course. I suspect thatr you haven't even gotten to the point where you've studied the math for that which requires tensor analysis. Is that correct?

I think Vision13 is suggesting that physicists take mathematical shortcuts that a mathematician would not take.

Originally Posted by KJW

Originally Posted by physicist

Originally Posted by Vision13

I'm learning calculus and analytic mechanics however i'm starting to think mechanics and more widely physics aren't rigorous.

That's certainly not true whatsoever! You just have a very long way to go before you can say that you know everything. Mechanics is a large subject and can't be learned in from one text in one course. I suspect thatr you haven't even gotten to the point where you've studied the math for that which requires tensor analysis. Is that correct?

I think Vision13 is suggesting that physicists take mathematical shortcuts that a mathematician would not take.

I was thinking that's true as well. In the intro physics courses things are modeled very differently from real life situations. That's probably what he must have in mind.

If you want rigor, try mathematical physics. A good chunk of it is proof and theorem.