More advanced physics is just the same with more maths

[ultrasmart]

More advanced physics is just the same with more maths!

Hi, I found a calculus textbook called Calculus 2000 at the following link http://www.physics2000.com/Pages/Calculus.html

They stated on their website :

the standard physics curriculum repeatedly goes over the same topics at successively higher mathematical levels

Is that statement true?

 

[Jack21222]

Hi, I found a calculus textbook called Calculus 2000 at the following link http://www.physics2000.com/Pages/Calculus.html

They stated on their website :

Is that statement true?

I'd say mostly true, yes. It also goes to more and more generalized cases. It just so happens that the general case requires higher level math than a case with a lot of symmetry or no friction, etc.

 

[TMFKAN64]

To a large degree, I can agree with this. After all, you study electricity and magnetism in freshman physics, and then again in an advanced electrodynamics course with a book like Griffiths. And then, if you go to graduate school, you will study it again with the book by Jackson. The situation is similar with mechanics, thermodynamics, optics, and even solid state physics.

However, it's not really repetition, it's going more in depth with each course.

 

[ultrasmart]

So is studying a book like Calculus 2000 eliminates the need to take classical mechanics, E&M, waves etc. courses after a typical introductory physics course? (The book is physics-based and it's available for free download on the link above)

 

[MarneMath]

No, not all. Just because you become aware that different methods can be used, does not mean you understand the benefit, the insight, and actual meaning.

 

[cytochrome]

The same topics are treated, but advancements make themselves clear because the math is more advanced.

For example, in a "general physics" course you can exhaust Newton's methods for a particle confined to stay on a surface until the differential equation for the law of motion becomes extremely difficult or impossible to solve numerically.

In an advance classical mechanics course, you will learn the Lagrangian method that relies on the energy of the particle and make your own constraints. The math involved is more complex and requires the student to have an understanding of variational calculus.This is just one example. Many problems become a lot more elegant and simpler with higher order of math that are required for many other formulations of mechanics.

There are also quantum mechanics and relatitivity, both of which require more mathematical maturity than classical mechanics as well.

 

[Choppy]

So is studying a book like Calculus 2000 eliminates the need to take classical mechanics, E&M, waves etc. courses after a typical introductory physics course? (The book is physics-based and it's available for free download on the link above)

I think you're reading quite a lot into a single, subjective statement in a textbook.

You won't get very far in physics if you start to believe that you can eliminate fundamental courses from your curriculum.

 

[Nabeshin]

"The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." -- Sidney Coleman

 

[Jorriss]

I don't really agree with that statement at all. My intro courses covered much of the physics of my upper division classical course, but not all of it, and not even close to all the physics in thermodynamics, statistical mechanics, E&M and quantum mechanics was covered in lower division courses.

A lot of the jump from undergraduate to graduate is in the mathematical maturity required, but not in the jump from LD to UD.

 

[WannabeNewton]

"The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." -- Sidney Coleman

Haha that is bloody brilliant. Anyways to the OP: couldn't you argue that adding more mathematical abstraction actually leads to a new way of understanding the same material? In that way the material might not be repetitive but would rather be augmented.

 

[chill_factor]

I disagree, there's actually new concepts, but they require math to know.

In QM, stat mech and thermo, that is especially true.

However some classes are just pure grinding math.

 

[Jack21222]

I disagree, there's actually new concepts,

The quote didn't say there weren't new concepts. It only said that there were concepts that are gone over repeatedly. I've learned quantum tunneling 3 times, for example. Same thing with Gauss's law, the harmonic oscillator, Lenz's law... the list goes on. It is quite obviously true that the physics curriculum repeatedly goes over these topics at higher mathematical levels.

Yes, there are also new topics, but that does not invalidate the fact that you learn many topics 3 times in physics.

 

[AlephZero]

The statement is "true", but content-free IMO. You might as well say that learning to play the piano, the whole curriculum just keeps going over how to play the same 88 notes.

Most of the physics curriculum, even at grad-school level, is taught using carefully chosen (i.e. articifially simplified) examples that can be solved with the limited math tools available to the student at each stage.

Even the math tools that grad-school physics students know are WAY to limited to solve most real-world problems. That's one reason most real-world problems are solved numerically not analytically.

 

[MathematicalPhysicist]

But we still have problems even in a matured subject such as classical mechanics. Look at the problem of Turbulence.

What we do in math and physics is to find something that we can solve in a reasonable time for publication (the publish or perish problem), instead of trying to actually solve something hard which may take more time and might be riskier for the academic career.

 

[zahero_2007]

Yes,but more complicated math is essential to solve more complicated problems .

 

[SophusLies]

The statement is "true", but content-free IMO. You might as well say that learning to play the piano, the whole curriculum just keeps going over how to play the same 88 notes.

This is a incredible analogy.

Even the math tools that grad-school physics students know are WAY to limited to solve most real-world problems. That's one reason most real-world problems are solved numerically not analytically.

This is also very true. Get some tools such as numerical analysis, PDE's and some computational programming skills and apply it to a nasty problem. If one modeled a spinning ball that is thrown through a variable wind speed, one would quickly find out how difficult of a problem that really is. I used to always try to model problems like these when I was an undergrad, I was consistently humbled by the shear amount of complexity of such problems.

 

[dextercioby]

Hi, I found a calculus textbook called Calculus 2000 at the following link http://www.physics2000.com/Pages/Calculus.html

They stated on their website :

Is that statement true?

Of course it is, mainly because the student preparing to be a physicist doesn't have the first 2 years of his whole academic studies filled with rigorous and difficult mathematics courses which should prepare him for a serious tackle of the physical theories (this would assume that everyone joining a physics department as a student wants to become a theoretical/mathematical physicist, which is obviously not true).

And of course, you have the typically US classification: undergraduate vs graduate. Namely, the graduate course on QM broadens the view on the whole theory you have gained a typical Schrödinger equation-based undergraduate course. The same goes for classical mechanics and electromagnetism.

 

[TMFKAN64]

So is studying a book like Calculus 2000 eliminates the need to take classical mechanics, E&M, waves etc. courses after a typical introductory physics course? (The book is physics-based and it's available for free download on the link above)

Since I previously said that the quote was essentially true, I want to add that this conclusion is completely wrong.

While I wouldn't go so far as to say the original quote was "content free", I would say that it's more an interesting observation about how physics is taught than anything that you can actually use to guide your studies.