I need some directions of books on classical mechanics

[anarchean]

Hi, I'm new to the forum, I'd like some recommendations of books on classical mechanics.

Too vague, right?

I'm a CS student, with a great disposition for mathematics and great love for physics.
I've learned one-variable calculus through Stewart and I'm starting linear algebra with Strang and differential equations.

I'm not a lecture kind of a guy, I like books. And I'm trying to learn physics by myself. Yeah, I know I can't do the experimental classes without a university, but let's leave that for the future me. (I want to study physics, but after I finish CS. I can't double major here in Brazil, unhappily.)

I want some recommendation of books on Classical Mechanics, with a strong emphasis on math. I started Goldstein's, but it looks really advanced, I was having some problems comprehending it. I went through Freeman and Young's University Physics (just the classical mechanics part).

Can any of you give me any tips or directions?
I'd be happy if I had to learn any more math, so, you can feel free to recommend any other math areas for me to learn, if you find it necessary.

Thank you very much for the time of anyone who can answer.

 

[micromass]

Kleppner & Kolenkow https://www.amazon.com/dp/0521198119/?tag=pfamazon01-20
This seems to be exactly what you're looking for. It only contains Newtonian mechanics, but is quite difficult and advanced. A strong knowledge of calculus is a must. Multivariable calculus is not needed.

 

[anarchean]

Cool! I'll try to get a copy. From what I've seen on Amazon it doesn't cover mechanical waves and fluid mechanics, do you think I should take some other book on these subjects? If so, do you have any recommendation?

 

[The Bill]

Waves and fluid mechanics are typically taught separately.

For classical mechanics, I recommend Marion and Thornton. You can get a copy of the 4th edition for very cheap, and I like the way they cover Lagrangian mechanics.

For fluids, I recommend Faber's Fluid Dynamics for Physicists. It handles the common situations in fluid mechanics with a good mix of intuition and physics-style rigor. Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris is a nice companion for the mathematical side of it.

I don't have any particular recommendations on wave mechanics textbooks. There are specialist texts on water waves, sound waves, shock waves, etc. Electromagnetic waves are handled in texts on electricity and magnetism, of course.

I would recommend working through the juicy bits of a text on partial differential equations, though. An intro differential equations course is enough preparation for intro classical mechanics like Marion and Thornton, but you need to understand Fourier analysis and partial differential equations to handle waves and fluids, etc.

 

[TSny]

A nice book on waves is Crawford's book: https://archive.org/stream/Waves_371/Berkeley3-Waves#page/n0/mode/2up

 

[anarchean]

Waves and fluid mechanics are typically taught separately.

For classical mechanics, I recommend Marion and Thornton. You can get a copy of the 4th edition for very cheap, and I like the way they cover Lagrangian mechanics.

For fluids, I recommend Faber's Fluid Dynamics for Physicists. It handles the common situations in fluid mechanics with a good mix of intuition and physics-style rigor. Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris is a nice companion for the mathematical side of it.

I don't have any particular recommendations on wave mechanics textbooks. There are specialist texts on water waves, sound waves, shock waves, etc. Electromagnetic waves are handled in texts on electricity and magnetism, of course.

I would recommend working through the juicy bits of a text on partial differential equations, though. An intro differential equations course is enough preparation for intro classical mechanics like Marion and Thornton, but you need to understand Fourier analysis and partial differential equations to handle waves and fluids, etc.

I see. So let me study them separately. About Marion and Thornton, it seen a little more advanced then Kleppner & Kolenkow (looking at the table of contents), maybe I should read it after K&K?

I'm studying differential equations now, although I still need to learn partial differentiation. Fourier analysis is something I have to study separately or is it related to differential equations?

About the fluid dynamics book: noted. I'll tackle classical mechanics first, but them I'll come back to this book (edit: those books).

 

[anarchean]

A nice book on waves is Crawford's book: https://archive.org/stream/Waves_371/Berkeley3-Waves#page/n0/mode/2up

Noted. Thanks TSny!

 

[The Bill]

Most math and physics majors I know first encountered Fourier analysis in the context of partial differential equations. If you want to study it separately, there are some really good books on it, but I think there might be advantageous to see it in the context of partial differential equations first.

Three good books are Tolstov's Fourier Series, Körner's Fourier Analysis(probably the best one to start with if you want to study Fourier series first) and Wilcox&Myers' An Introduction to Lebesgue Integration and Fourier Series, which I'd recommend reading after you feel somewhat comfortable with Fourier series in practice. The Lebesgue integral formulation opens up a lot more classes of functions for representation as Fourier series, and also clarifies and codifies some of the "special rules" of Fourier series that have to be more or less taken on faith in the earlier places they're encountered.

Oh, and the book I first learned PDEs out of is Snider's Partial Differential Equations: Sources and Solutions. Used copies of it are really cheap. It's an alright book. I don't have any cautions against it, at least. I don't have any significantly better recommendations.

Looking at Kleppner & Kolenkow, yes it is a lot more basic than Marion and Thornton. Kleppner & Kolenkow seems to be on the same level as a standard Physics I, II, and III text(physics with calculus in some universities.) So, if you've already had calculus based physics, skip Kleppner & Kolenkow. It seems like a fine introduction to mechanics if you haven't had any calculus based physics, though. I'd recommend supplementing it with Feynman's lectures: http://www.feynmanlectures.caltech.edu/

Based on your list of topics of interest, I'd also recommend you get a copy of Strogatz' Nonlinear Dynamics and Chaos. It helps fill in a lot of the gaps left after learning mechanics the usual way. Getting a good feel for how to deal with problems that stray from the idealized "massless this, frictionless that" assumptions is quite helpful. Also, Strogatz' presentation is fun and practical. A series of Strogatz' lectures teaching out of this book are also available on YouTube:

 

[anarchean]

I think I'm going to a PDE text. I can go deeper after that. But thanks for the recommendations.

I'll try to read a little of the two books and see if I'm comfortable with Marion & Thornton.

And I'm totally going to read the Feynman's lectures, I forgot about it. I read a little, it's a really cool text.

Wow, Strogatz' seen really cool, I'll also check this out.

Thank you very much for your help. Got the directions I wanted. I think the rest is with me.
I hope I'm not being too annoying, but since we're in it, do you have any suggestion for ODE? I'm currently using Boyce and DiPrima's Elementary Differential Equations and Boundary Value Problems, do you think there is a better text?

 

[The Bill]

Boyce and DiPrima is fine. As you're working through it just realize that most of the special methods taught are fluff that rarely get used in practice. What you should really understand after studying differential equations is linear differential equations with constant coefficients, and the practical use of Laplace transforms.

Edit: oh, and for all of the topics in this thread, make sure your fundamental understanding of linear algebra is strong. You will benefit greatly from a good understanding of practical matrix calculations, and also of the axioms and applications of abstract vector spaces and linear operators.

 

[anarchean]

Boyce and DiPrima is fine. As you're working through it just realize that most of the special methods taught are fluff that rarely get used in practice. What you should really understand after studying differential equations is linear differential equations with constant coefficients, and the practical use of Laplace transforms.

I'll focus on that then.

Edit: oh, and for all of the topics in this thread, make sure your fundamental understanding of linear algebra is strong. You will benefit greatly from a good understanding of practical matrix calculations, and also of the axioms and applications of abstract vector spaces and linear operators.

Cool. Thank you very much.

 

[marcusl]

I used Boyce and di Prima and liked it. Didn't like my PDE book much but found Farlow's book on PDE's to be good for self study and inexpensive (Dover). I like Meyer's book on matrix and linear algebra--it's practical and physical rather than abstract and mathematical.

 

[MidgetDwarf]

I liked Strauss partial differential equations..

 

[anarchean]

marcusl
Nice... I like Dover, generally. About linear algebra I think Strang is doing OK for me, after I finish it I'll seek for something else.MidgetDwarf
Thanks. I'll take a look.

 

[smodak]

A nice but inexpensive PDE book is
https://www.amazon.com/dp/048667620X/?tag=pfamazon01-20

 

[TSny]

Didn't like my PDE book much but found Farlow's book on PDE's to be good for self study and inexpensive (Dover).

A nice but inexpensive PDE book is
https://www.amazon.com/dp/048667620X/?tag=pfamazon01-20

Yes, I think Farlow is a great choice for self-study if you are looking for an introductory, practical approach to methods of solving various types of PDE's.