Good book for First Course in Calculus based Classical Mechanics

In summary, K&K should be enough, but if there is difficulty, it would be with the multivariable calculus.
  • #1
tridianprime
102
2
I have taken a look at Kleppner and Kolenkow and that seems around the right level of difficulty but I was wondering if there were any other books that worked well alongside the Walter Lewin lectures on OCW. Would K&K?

Also, where does K&K go up to? Does it include all undergraduate Classical Mechanics or just 1/2nd year? Could you go from this to say a graduate text?

I am looking for general feedback for K&K but also recommendations of books that I could use and could you please tell me which books are lower or upper level and if they cover all undergrad material. Finally, is Taylor's book appropriate for undergrad or just lower or just upper level? If it's upper level, could you use K&K before, if K&K is lower level(?). I am sorry for the unorganised nature but I am just trying to get a better picture of what approaches I could take.
 
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  • #2
MIT OCW has a course 8.012 that uses K&K, there are lecture notes and assignments. And if you look at the calendar for 8.01 and 8.012, you can perhaps see how they compare. K&K is regarded as a difficult book because it uses calculus throughout and has derivations in lieu of explanations. But if one knows calculus very well, the math is a language that explains better than words can.

The closest book to the first Walter Lewin course would almost certainly be Newtonian Mechanics by French, I think he was a previous teacher of that subject. Professor Lewin uses some of his materials in the videos, usually diagrams for the overhead.

I don't know enough to answer your other questions.
 
  • #3
verty said:
MIT OCW has a course 8.012 that uses K&K, there are lecture notes and assignments. And if you look at the calendar for 8.01 and 8.012, you can perhaps see how they compare. K&K is regarded as a difficult book because it uses calculus throughout and has derivations in lieu of explanations. But if one knows calculus very well, the math is a language that explains better than words can.

The closest book to the first Walter Lewin course would almost certainly be Newtonian Mechanics by French, I think he was a previous teacher of that subject. Professor Lewin uses some of his materials in the videos, usually diagrams for the overhead.

I don't know enough to answer your other questions.

That 8.012 course actually looks good. However, there are only a few lectures. I also notice that it misses out some topics in K&K such as relativistic kinematics. Would you suggest I just complete K&K without Lewin lectures or with? Would K&K alone be enough to then study some electromagnetism i.e. Purcell? Thanks.
 
  • #4
tridianprime said:
That 8.012 course actually looks good. However, there are only a few lectures. I also notice that it misses out some topics in K&K such as relativistic kinematics. Would you suggest I just complete K&K without Lewin lectures or with? Would K&K alone be enough to then study some electromagnetism i.e. Purcell? Thanks.

Oh sorry, I didn't realize there weren't lecture notes for that course, usually the notes are pretty good, as good as the videos.

Definitely with the Lewin lectures, I think they are very entertaining.

K&K should be enough, you could always ask questions if something is not making sense. It does progressively use more and more calculus, for example eventually using multiple integrals for center of mass, as well as Stokes' theorem. This is all math needed for Purcell anyway so I think it is good to see it early. I believe the authors intended their book to be usable by students who are learning multivariable calculus at the same time.

If there is any difficulty, I expect it to be with this multivariable calculus. But my advice there is to remember that it is just an extension of calculus to multiple dimensions, everything has its higher-dimensional analogue. The tangent, the gradient, they are all present and work in similar ways, so thinking "how does this compare to the single-variable case" is, I believe, the right way to learn it.

I don't think K&K is as difficult as it'll look to many people, it is supposed to be an easier way to learn by using more advanced math to be more accurate. I think you could definitely proceed to Purcell afterwards, you would have used some of the math already and should be well prepared.

To go further with mechanics, you would need a Lagrangian/Hamiltonian book. This is not a topic I know much about except that it is difficult. Taylor's book seems to be half revision/half new content, probably there would be some overlap with K&K, there is probably a more direct path.

I suppose it can't hurt to give a possible book:

https://www.amazon.com/dp/0486630692/?tag=pfamazon01-20.
 
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  • #5
verty said:
Oh sorry, I didn't realize there weren't lecture notes for that course, usually the notes are pretty good, as good as the videos.

Definitely with the Lewin lectures, I think they are very entertaining.

K&K should be enough, you could always ask questions if something is not making sense. It does progressively use more and more calculus, for example eventually using multiple integrals for center of mass, as well as Stokes' theorem. This is all math needed for Purcell anyway so I think it is good to see it early. I believe the authors intended their book to be usable by students who are learning multivariable calculus at the same time.

If there is any difficulty, I expect it to be with this multivariable calculus. But my advice there is to remember that it is just an extension of calculus to multiple dimensions, everything has its higher-dimensional analogue. The tangent, the gradient, they are all present and work in similar ways, so thinking "how does this compare to the single-variable case" is, I believe, the right way to learn it.

I don't think K&K is as difficult as it'll look to many people, it is supposed to be an easier way to learn by using more advanced math to be more accurate. I think you could definitely proceed to Purcell afterwards, you would have used some of the math already and should be well prepared.

To go further with mechanics, you would need a Lagrangian/Hamiltonian book. This is not a topic I know much about except that it is difficult. Taylor's book seems to be half revision/half new content, probably there would be some overlap with K&K, there is probably a more direct path.

I suppose it can't hurt to give a possible book:

https://www.amazon.com/dp/0486630692/?tag=pfamazon01-20.

Thanks a lot. I will go with K&K with Lewin. As far as multivariable calculus, that is no problem because I am currently working through Hubbards book.

As for Langrangian mechanics, I have a book I bought by accident by Kibble and Berkshire that is meant for upper level courses I think and includes such topics so I can use that when I am ready.
 
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  • #6
How is that Hubbard book by the way? Does it have good exercises? By good I mean, are they helpful for understanding?

(I did some editing here to make the language better)
 
  • #7
verty said:
How is that Hubbard book by the way? Does it have good exercises? By good I mean, are they helpful for understanding?

(I did some editing here to make the language better)

I think it is brilliant. There are plenty of exercises at the end of each chapter and they greatly helped my understanding. It is also written in a very inspiring and motivating way I found that makes you interested in constantly advancing to the next exercise or page. Highly recommended!
 
  • #8
Oh right, so it's actually a good book. I thought any book with "differential forms" in the title wouldn't be good. It just goes to show, there are many books out there and there are many variations on a theme. It's amazing how many different books and styles there can be for a single subject. In a way it's and in a way it's bad. All books should be the same, it would be easier (in the sense that too much choice can be debilitating).
 
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  • #9
I agree that they should be organised and labeled in some way as well. However, I am sorry if I am sounding naive but what is wrong with "differential forms"? It's just multivariable calculus free of a co-ordinate system isn't it? I think it's seen as a more rigorous approach(?).
 
  • #10
With all I have praised it, it is worth bearing in mind that I am self studying it without the aid of an instructor and I feel this book is great for that. I have read that it can be a bit slow otherwise(?) and that Spivak is a better option. However, I was under the impression that Spivak did not include as much and wasn't suitable for a multivariable calculus course. Do you know if this is correct?
 
  • #11
I know absolutely nothing about Spivak's manifolds book. I know he wrote that and 5 volumes of differential geometry, so clearly that is his speciality.

I wouldn't say that differential forms are a more rigorous approach, I mean I don't know that much about them but it looks to me like a more concise notation. But I don't know about pullback and all that, I suppose there must be some elegance to it. But let's take Hubbard's book for example. I grant you that it is a good book about differential forms, but the title suggests it is for vector calculus and linear algebra only. Both of those are pretty elementary subjects. So if one is learning these forms just to be able to do the same old same old, then any such book should be a more difficult way to learn.

This was my thinking. And I wondered about the exercises, if they reduced the difficulty of the material. But I believe you that they do. So it's another book on the pile of books for multivariable calculus. There are ones called "Advanced Calculus", ones called "Multivariable Calculus", ones called "Vector Calculus", ones called "Vector Analysis", ones called "Calculus of Several Variables". And ones called "Calculus", like Courant and Apostol. It's amazing how many books there are, is all.

Something different now. I seem to remember but I can't confirm it by searching, either the old threads are gone or it was someone else. But I seem to remember that you were someone who bought University Physics. And now you are asking about K&K, but these books obviously do overlap. So I just thought if it was you, perhaps you thought K&K was at a higher level, whereas I don't think it is necessarily, it just uses calculus more openly from the start and has some more detailed derivations. But you could learn mechanics from the other book as well.

Or I could be mistaken and it was somebody else.

Edit: I'm starting to realize that maybe Hubbard intended his book to be just another multivariable book, but using this new notation. So actually in that case it won't be what I thought, a kind of second book on the subject. So actually, it probably is pretty good because it makes it quicker to learn this new notation. So I think I was on another page entirely.
 
  • #12
I'll write this here to so that I can link to it in future. With regard to K&K versus a book like University Physics, it is important to make a distinction between the language of a book and the subject of a book. The language of a book is what level of math it uses. The math is part of the language used to describe the subject of the book. So a graduate book will used more advanced language because the reader knows more advanced math.

The subject of a book is what the book is trying to teach you. So with these two books, both have been used at MIT, both (as far as Newtonian mechanics goes) are trying to teach you the same things, the subject is the same. The language is slightly different because K&K uses calculus very openly. UP also does but it can be skipped because it is meant for high school students now entering college. So it is slower going but does include some derivations and does include some calculus problems.

So by this categorization, the subject is the same but the language is slightly different, but I would say not different enough to need both. UP covers relativity even, it really does overlap almost entirely with K&K. And this is true with VERY MANY books. On anyone subject there are way many books, but usually most of the difference is language, they will generally teach the same topics although some will go further or into more detail. But there is really no perfect book, there are just books that use language that you understand and teach what you want to learn, and beyond that it is down to effort and dedication to work through them.

And of course we can judge books by how well they enable one to self-study. By this standard, the Hubbards book mentioned earlier sounds good indeed. The language of that book may be at a higher level but it is another multivariable book, it'll teach that subject along with some new notation. Hence why I lament the number of books, there really should be fewer.

That is all.
 
  • #13
I don't think that was me. I considered University Physic sat one point and I may have spoken out of context but I don't think even that - I had a look at past posts to see if I spoke out of context.

Yes, there are a lot of such books. I did look around quite a bit though and this definitely seems to be the best and most comprehensive book on multivariable calculus, even if it has a few minor flaws. Which books don't?

Having a look at later chapters, it goes into a number of forms topics in Chapter 6. I think that Hubbard is also quite versatile in that a variety of people can use it. If you want a rigorous treatment you can use the appendixes at the end that delve into "harder proofs", as he puts it, so I think it will be quite useful for someone wanting a book like Spivak, like myself. I actually mentioned this on the textbook listing thread for this book.
 
  • #14
Interesting, so would you want fewer books at the same level or just fewer levels of depth for a subject. Sorry, if that make little sense and I have misunderstood you.
 

1. What is the best book for a first course in calculus-based classical mechanics?

The best book for a first course in calculus-based classical mechanics is subjective and can vary depending on personal preferences and teaching styles. Some popular options include "Classical Mechanics" by John R. Taylor, "An Introduction to Mechanics" by Daniel Kleppner and Robert Kolenkow, and "Classical Mechanics: Systems of Particles and Hamiltonian Dynamics" by Walter Greiner.

2. What topics should be covered in a first course in calculus-based classical mechanics?

A first course in calculus-based classical mechanics should cover basic principles such as Newton's laws of motion, conservation of energy and momentum, rotational motion, and gravitation. It should also introduce students to the use of calculus in solving problems in classical mechanics.

3. Is prior knowledge of calculus required for a first course in calculus-based classical mechanics?

Yes, a solid understanding of calculus is necessary for a first course in calculus-based classical mechanics. This includes knowledge of derivatives, integrals, and basic concepts such as limits and continuity.

4. Can a first course in calculus-based classical mechanics be self-taught?

While it is possible to self-study calculus-based classical mechanics, it is not recommended. This subject can be challenging and having an experienced instructor to guide you can greatly enhance your understanding and problem-solving skills.

5. Are there any online resources available for a first course in calculus-based classical mechanics?

Yes, there are many online resources available for a first course in calculus-based classical mechanics. Some popular options include lecture videos on platforms like YouTube and Khan Academy, interactive simulations and demonstrations, and online textbooks or lecture notes.

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