Is Physics Just Solving DEs? Undergrad Perspective

[qspeechc]

Am I wrong, or is physics just about solving differential equations? I am nearly at the end of my secon year as an undergrad, and it seems to me that all I've been doing this year is solving DEs in physics. Is this all physics is about? If I carry on with physics, to postgrad, is this what I will be doing all the time, solving differential equations? A final year student told me she thinks physics is just a branch of applied maths, I think I agree.

Side Note: Why then, don't we have a year whn we are just taught the maths we need: calculus, linear algebra, DEs before we start o physics.

 

[Oberst Villa]

A final year student told me she thinks physics is just a branch of applied maths, I think I agree.

I would disagree. Math, whether applied or not, is about proving stuff. Some guy proves a mathematical law, and then it's true and it remains true until hell freezes.

Physics is much more fun: You make some observation of nature, and if you are lucky you find a law that correctly describes these observations and predicts some other observations. Now if the stuff that was predicted is really observed, then you can say that the law is "true". But there is a good chance that some decades or centuries later some new observations will be made that do not quite fit this law. Then you have to think again, and you might discover that the old law was just an approximation of a new, more general law.

What I'm trying to say is, in physics there might always be a surprise waiting for us, so its very distinct from math and definitely more fun.

 

[cesiumfrog]

If you're more interested in the mathematical techniques than the physical significance of the results, why don't you study mathematics instead? Otherwise, just find some software to solve the ODE's for you.

 

[rcgldr]

In real life it gets worse. Many things, like ballistics, involve differential equations that are too difficult to solve directly, so numerical integration is required. Also in the case of ballistics, the physics of near and above mach air speeds is too difficult to decribe as a single differential equation, so tables are required as well. (Glad I'm a programmer, it's easier).

 

[atyy]

A final year student told me she thinks physics is just a branch of applied maths, I think I agree.

I have no idea whether Hawking believes he is holding the right title
http://en.wikipedia.org/wiki/Lucasian_Professor_of_Mathematics

An interesting interview with James Lighthill:
http://www.lucasianchair.org/papers/lighthill-interview.html

 

[Hurkyl]

I would disagree. Math, whether applied or not, is about proving stuff. Some guy proves a mathematical law, and then it's true and it remains true until hell freezes.

Math is also about figuring out what to prove, as well as developing effective methods for solving problems. I've once heard the essence of theorem proving summarized as follows: "First, you figure out what ought to be true, and then you figure out how to ensure that it really is true."

 

[rcgldr]

developing effective methods for solving problems.

Being a programmer that has worked with Reed-Solomon type error correcting codes, a sub-set of finite math, I can attest to the fact that a lot of research in this area was been aimed at improving efficiency (although now that gates in a chip are almost free when compared to pin count, a lot of implmentations can replace efficient algorithms with more and larger tables). It was interesting working with algorithms that are only decades old instead of centuries.

 

[vanesch]

I guess that by far most working physicists also have something to do with experimentation and instrumentation. Pulling experimental gear together, or filling in order forms, or scanning through instrument specifications is not solving differential equations.

 

[uart]

Side Note: Why then, don't we have a year whn we are just taught the maths we need: calculus, linear algebra, DEs before we start o physics.

Most degree programs do have a fair amount of maths topics in the first two years. What maths subjects do you currently have in your degree program?

 

[qspeechc]

Nobody has answered my question. Is the purely theoretical side of physics all about solving DEs?

Oberst Villa: applied maths, in my experience, is not so much about rigour like pure math is. Applied maths is: differential equations, numerical methods etc. which seems to be pretty much all that physics is.

cesiumfrog: I am actually a mthematics major, but there is a small chance I will switch to physics.

atyy: thanks for the links

vanesch: point well taken. I guess most physics work is not theoretical. Actually I don't know; it's just a guess. What is post-grad in physics actually like? DEs is my guess.

uart: what I meant was the first year should be dedicated to pure and applied maths only, nothing else. How much easier would physics be then? Get done with calculus, DEs, linear algebra, numerical analysis and whatever else they can cram in, then one can really tackle physics.

I have taken: calculus, single- and multi-variable; linear algebra; ODEs; right now I'm busy with PDEs, numerical analysis, real analysis and abstract algebra. Does that sound about right?

 

[uart]

I have taken: calculus, single- and multi-variable; linear algebra; ODEs; right now I'm busy with PDEs, numerical analysis, real analysis and abstract algebra. Does that sound about right?

Yeah that sounds about right. The Maths is typically spread over the first two years of the degree. I think most student would prefer it that way rather than trying to cram all the maths into one year, (though that's just my opinion).

 

[Enjolras1789]

No, physics is much more than solving differential equations. I personally find this a ridiculous notion. Solving problems in textbooks might mean solving differential equations. Solving problems in textbooks is not being a physicist. Being a physicist requires studying nature, trying to understand that which is not understood. What is new (meaning not fully described) by definition does not have a differential equation to solve. One must understand and study what is going on physically, develop some sort of model, then test the model. Testing the model may include solving differential equations or some other maths...but the true challenge is in deciding how to describe the problem, how to set up the equations, how to understand processes that are counter-intuitive.

The men and women who founded quantum mechanics and special relativity didn't do so by solving differential equations. They looked at experimental evidence, thought about the physical meaning, and developed models of the world that went completely against all physical intuition. They defined the framework that students learn to solve problems in; they are the true heroes of physics.

Mathematicians don't care what the rules of the game of life really are; they systematically explore the consequences of all possible rules one might consider, in every possible set of postulates and assumption. Physicists try to determine what the rules of real life are (and then may need help from mathematicians to work out the consequences of those rules mathematically).