Differential Equations for Physics

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Discussion Overview

The discussion revolves around the importance and relevance of differential equations (DEs), particularly ordinary differential equations (ODEs) and partial differential equations (PDEs), in the context of physics education and careers. Participants explore whether it is worthwhile to invest time in studying DEs from a mathematical perspective, especially for physics majors considering graduate school.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants express a lack of interest in DEs, finding them boring and aesthetically unpleasing, yet acknowledge their importance in technical fields.
  • One participant emphasizes that understanding ODEs and PDEs is crucial for a successful career in technical fields, questioning the validity of opinions suggesting they are unnecessary.
  • Another participant outlines four aspects of DEs: numerical solutions, analytic solutions, qualitative analysis, and abstract theory, highlighting the importance of numerical solutions for engineers and the necessity of understanding analytic solutions for physicists.
  • A participant suggests that physics majors will encounter ODEs and PDEs extensively in graduate school, implying that proficiency in these areas is essential.
  • There is a discussion about whether to learn DEs through physics texts or dedicated math texts, with some advocating for formal study rather than informal learning on the fly.
  • Several participants recommend taking courses in both ODEs and PDEs, reinforcing the idea that formal education in these subjects is beneficial.

Areas of Agreement / Disagreement

Participants generally agree on the importance of DEs for physics majors, particularly those planning to attend graduate school. However, there is disagreement on the best approach to learning DEs, with some advocating for formal courses and others suggesting self-study through various texts.

Contextual Notes

Some participants express uncertainty about their understanding of DEs, indicating that there are gray areas in their knowledge. The discussion reflects varying levels of comfort and familiarity with the subject matter among participants.

Who May Find This Useful

This discussion may be useful for physics students, particularly those considering graduate studies, as well as educators and professionals in technical fields who are evaluating the role of differential equations in their work.

Astrum
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My weak spot in math is certainly DEs, I find them pretty boring, and fairly unattractive from an aesthetic point of view.

I've spent some time with them while studying harmonic motion, and I've gotten OK at them when applied to this particular topic (aside from having trouble with solving driven oscillatory motion), but when applied to other areas, I still have much trouble (PDEs are the worst).

So the question I ask is, is it worth spending time on them from a mathematical point of view? I understand that most universities require a semester or two on ODEs and PDEs, but I've heard people complaining that such classes are not necessary.
 
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If you don't understand ODEs and PDEs, your career in just about any technical field will be severely limited. I don't know who you've been talking to (humanities majors perhaps?) and I don't know what you are studying or what career you hope to enter.
 
I also think DEs are boring and aesthetically displeasing.

They are, however, important.

There are basically four different "aspects" of DEs (whether O or P):
  1. Numerical solutions
  2. Analytic solutions
  3. Qualitative analysis
  4. Abstract theory

The first is very important for anyone doing engineering and for most people doing physics. There are probably mathematicians who study DEs who have no idea how to numerically solve them, but everyone else who uses them needs to be adept at solving them numerically using computers.

The second and third are probably good for everyone to know. Engineers might be able to get away with just doing simulations without any understanding, but physicists probably can't. And even then, knowing what the solution should look like will be informative. From my perspective as a mathematician (not a working physicist or engineer), at the very least, you should study this topic from a mathematical perspective until you don't have trouble with inhomogeneous second-order linear ODEs with constant coefficients (e.g. driven oscillators). You should also be able to look at linear PDEs (wave/heat/Schrödinger's equations, etc.) without running away in terror. And that is a minimum.

The abstract stuff is almost exclusively the territory of mathematicians, and specifically analysts. I would not recommend spending your valuable time and energy on it unless you think you may fall into that category, or just want to see what analysts do all day.
 
SteamKing said:
If you don't understand ODEs and PDEs, your career in just about any technical field will be severely limited. I don't know who you've been talking to (humanities majors perhaps?) and I don't know what you are studying or what career you hope to enter.

Physics major, who hopes to one day go to grad school.

I KINDA understand DEs, with a lot of gray areas. I know I need to get better at them, my question is really "Do you think it would be worth my time to go through a math text on DEs".
 
If you are a physics major headed to grad school, you will undoubtedly be showered with ODEs and PDEs until you can't stand it. If you can't handle them, it would be like an eye doctor who can't see.
 
SteamKing said:
If you are a physics major headed to grad school, you will undoubtedly be showered with ODEs and PDEs until you can't stand it. If you can't handle them, it would be like an eye doctor who can't see.

Yeah, I understand that, but it wasn't really my question.

Should I just try to pick up DEs as I go along (from physics texts), or would I benefit from studying from a math text that deals with DEs (such as this)
 
I would use whatever text you feel comfortable with (IDK if there is an 'ODEs for Dummies'). I am curious how you managed to major in physics without taking at least one class in DEs. Even engineering majors take at least a one semester course. I don't recommend you pick stuff up 'on the fly' as it were. You are now in school; the courses you take should be focused on getting your degree. If you are not sure of what courses to take, consult a faculty advisor and not some random people.
 
I hope this can help

Astrum, I am writing articles to try to help people just like you. I am actually writing an article as I reply to you about Differential Equations used in Beam Deflection (in this case an F1 Front Wing). It won't be done for several hours, but you can find my list of applications for math here.

Applied Math Examples List - Methods - Real World Uses

Let me know if this is helpful for you in general, and I'll reply when my DiffE article is done.

I think most people struggle with math because they don't see the direct real world uses for it.


fr_wing_cantilevered_deflection.png
 
Simple answer to a simple question. YES. take courses in both ODE's and PDE's.
 
  • #10
Integral said:
Simple answer to a simple question. YES. take courses in both ODE's and PDE's.

Ok, that's all I was looking for. :thumbs:
 

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