Topics covered in John R Taylor Classical mechanics

[bigmike94]

TL;DR Summary

What topics are covered.

I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics? Would it be similar to what’s covered in Newtonian mechanics, but obviously more advanced.

Cheers in advance 👍

 

[kuruman]

I am looking at my copy from a few years back, 2005 copyright.

It covers all of the standard topics in Newtonian mechanics, 11 chapters, starting with Newton's laws of motion and ending with coupled oscillations and normal modes. Then it has an additional 5 chapters of "Further Topics" which are: Non linear mechanics and chaos, Hamiltonian mechanics, collision theory, special relativity and continuum mechanics.

Its level is intermediate, i.e. requires 2 semesters of intro physics, 3 semesters of calculus and (ideally) a course in linear algebra and ordinary differential equations. I adopted it for my course in Classical Mechanics, I loved it and so did my students. I covered only about half of it as it is obviously intended for a two-semester sequence. I still consult with it even though I am no longer teaching. I highly recommend it.

 

[bigmike94]

I am looking at my copy from a few years back, 2005 copyright.

It covers all of the standard topics in Newtonian mechanics, 11 chapters, starting with Newton's laws of motion and ending with coupled oscillations and normal modes. Then it has an additional 5 chapters of "Further Topics" which are: Non linear mechanics and chaos, Hamiltonian mechanics, collision theory, special relativity and continuum mechanics.

Its level is intermediate, i.e. requires 2 semesters of intro physics, 3 semesters of calculus and (ideally) a course in linear algebra and ordinary differential equations. I adopted it for my course in Classical Mechanics, I loved it and so did my students. I covered only about half of it as it is obviously intended for a two-semester sequence. I still consult with it even though I am no longer teaching. I highly recommend it.

Thank you for the reply. I am looking forward to getting stuck into it.

I’m not too far off now. Few chapters remaining on Newtonian mechanics and I’ve just started linear algebra, differential equations and multivariable calculus.

 

[kuruman]

Are you contemplating self-study? If so, it is better in that regard than other textbooks I have seen.

 

[bigmike94]

Are you contemplating self-study? If so, it is better in that regard than other textbooks I have seen.

Yeah I am self studying. Well mostly, I am technically on a physics degree, but it is part time and at the moment I’m only doing a maths module. I won’t be starting their main physics modules till next year. I am trying to stay ahead of the university modules because sometimes I feel it’s rushed, you’re starting a new topic before fully understanding the one before.

I think with this in mind I will probably try hurry things up with the remaining Newtonian chapters, as I’ll have to re do them all next year with university anyway.

 

[bigmike94]

Are you contemplating self-study? If so, it is better in that regard than other textbooks I have seen.

While I have got you here. I have spent quite awhile building up a solid foundation on Newtons laws and the conservation of energy stuff. As I have heard somewhere that those are the main theme in classical mechanics such as John Taylor’s. How true is this? How well is stuff thought from first principles in Taylor’s book? Or does it kind of gloss over the stuff you should know.

Basically I am asking can you learn from that book given that you have the maths background and know basic Newtonian mechanics. Does it teach the topics well from scratch

 

[kuruman]

While I have got you here. I have spent quite awhile building up a solid foundation on Newtons laws and the conservation of energy stuff. As I have heard somewhere that those are the main theme in classical mechanics such as John Taylor’s. How true is this? How well is stuff thought from first principles in Taylor’s book? Or does it kind of gloss over the stuff you should know.

Basically I am asking can you learn from that book given that you have the maths background and know basic Newtonian mechanics. Does it teach the topics well from scratch

"From scratch" is relative. The acquisition of knowledge is incremental. When kids learn how to add and subtract in first grade, they are supposed to have learned how to count in kindergarten. Likewise, when you reach the intermediate level in physics, you are expected to have learned something at the introductory level. I quote from the preface of the book. Taylor is talking about the students whom he taught out of this book at his institution.

"$\dots~$ Almost all of these students have taken a year of freshman physics, and so have at least a nodding acquaintance with Newton's laws, energy and momentum, simple harmonic motion, and so on. In this book I build on this nodding acquaintance to give a deeper understanding of these basic ideas, and then go on to develop more advanced topics, such as the Lagrangian and Hamiltonian formulations, the mechanics of noninertial frames, motion of rigid bodies, coupled oscillations, chaos theory and a few more."

As you can see, he is well aware that the users of his book have not mastered the material, yet they have the basics which he can then proceed to reinforce. For example, the first equation in the book is the position vector, $$\mathbf{r}=x\hat{\mathbf{x}}+y\hat{\mathbf{y}}+z\hat{\mathbf{z}}$$He assumes you have seen this before and does not explain the idea of a unit vector. However, he shows other ways to express unit vectors, such as $~\{\hat{\mathbf{i}},~\hat{\mathbf{j}},~\hat{\mathbf{k}}\}~$ and $~\{\hat{\mathbf{e}}_1,~\hat{\mathbf{e}}_2,~\hat{\mathbf{e}}_3\}~$ and then summarizes vector operations (addition, multiplication, dot and cross product). What he is saying here is "I assume that you have seen all this before and that you understand what I'm saying. However if you don't, then you have to figure it out and/or relearn it from somewhere else. He is not going to teach you the concepts of unit vectors, vector addition and multiplication because that's where he draws the line separating what constitutes "from scratch" and what doesn't.

I hope this helps.

 

[bigmike94]

"From scratch" is relative. The acquisition of knowledge is incremental. When kids learn how to add and subtract in first grade, they are supposed to have learned how to count in kindergarten. Likewise, when you reach the intermediate level in physics, you are expected to have learned something at the introductory level. I quote from the preface of the book. Taylor is talking about the students whom he taught out of this book at his institution.

"$\dots~$ Almost all of these students have taken a year of freshman physics, and so have at least a nodding acquaintance with Newton's laws, energy and momentum, simple harmonic motion, and so on. In this book I build on this nodding acquaintance to give a deeper understanding of these basic ideas, and then go on to develop more advanced topics, such as the Lagrangian and Hamiltonian formulations, the mechanics of noninertial frames, motion of rigid bodies, coupled oscillations, chaos theory and a few more."

As you can see, he is well aware that the users of his book have not mastered the material, yet they have the basics which he can then proceed to reinforce. For example, the first equation in the book is the position vector, $$\mathbf{r}=x\hat{\mathbf{x}}+y\hat{\mathbf{y}}+z\hat{\mathbf{z}}$$He assumes you have seen this before and does not explain the idea of a unit vector. However, he shows other ways to express unit vectors, such as $~\{\hat{\mathbf{i}},~\hat{\mathbf{j}},~\hat{\mathbf{k}}\}~$ and $~\{\hat{\mathbf{e}}_1,~\hat{\mathbf{e}}_2,~\hat{\mathbf{e}}_3\}~$ and then summarizes vector operations (addition, multiplication, dot and cross product). What he is saying here is "I assume that you have seen all this before and that you understand what I'm saying. However if you don't, then you have to figure it out and/or relearn it from somewhere else. He is not going to teach you the concepts of unit vectors, vector addition and multiplication because that's where he draws the line separating what constitutes "from scratch" and what doesn't.

I hope this helps.

Ah yes that helps a lot 👍 I’m “quite” familiar with vectors, Newtons laws, energy etc.

Maybe I’m closer than I originally thought to being able to comprehend the book. No rush though 😃

 

[kuruman]

Good luck and don't forget we are here in case you get stuck.

 

[berkeman]

Summary: What topics are covered.

I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics?

I did a Google search on classical mechanics by taylor -- table of contents and the 2nd hit on the list has the Table of Contents as one of the tabs:

https://uscibooks.aip.org/books/classical-mechanics/

 

[bigmike94]

I did a Google search on classical mechanics by taylor -- table of contents and the 2nd hit on the list has the Table of Contents as one of the tabs:

https://uscibooks.aip.org/books/classical-mechanics/

View attachment 302615

Must have missed this, thank you 👍