Learn Math & Physics: How to Go Forward

[tridianprime]

I am reading Spivak as i love pure mathematics and want to go in that direction but i also want to learn physics as well. I would like to learn classical mechanics. Do you think i should wait to finish spivak first and then do this or can i do them both at the same time as a lot of the work in spivak isn't used in physics. What do you think i should as i am getting stressed and anxious for some reason.

Also, i have trouble just sitting down and reading the textbook. It just feels uncomfortable and i get distracted. However, i am really interested and want to learn it. I just need to get a structure in my head of what to do.

 

[CompuChip]

I'm not very familiar with Spivak, but basic physics like classical mechanics does not require a very detailed mathematical understanding. Usually, physicists handle their mathematics quite loosely, assuming for example that functions are sufficiently smooth to take limits and sweeping discontinuities under the carpet every now and then :-)

I guess the bigger issue would be whether you have time to do those two things at the same time.

 

[tridianprime]

In that case, what books would you recommend for an undergrad course in CM from freshman to whatever the last year is in the states(I'm uk).

 

[Shivam3013]

Hi tridianprime;
Spivak calculus is a very rigorous book. After completing it, if you are interested in pure math, then you might benefit from reading Apostle or Courant. Those cover similar material, just a more rigorous treatment of the subject. As for physics, CM is what you should start with. Halliday, Resnick doesn't require much calculus, but I didn't like the book. I would recommend a book such as Kleppner/Kolenkow or Morin. The latter is however more rigorous, and what I recommend. However, Morin assumes a bit more calculus knowledge then what you may have encountered. Therefore, you have two options:

Read spivak and kolenkow simultaneously
or
Finish spivak then read morin

One thing you have you understand is that you can do them both. After the former option, morin might seem like a review. The same goes for reading apostle or courant after Spivak.

 

[tridianprime]

Thank you, I'll work hard on spivak and then do moron as actually started reading that after the Harvard recommendation but it was a bit hard to grasp.

 

[WannabeNewton]

Morin is very hard if you've never had a mechanics class before. Doing spivak will not help you in the least bit in getting through Morin successfully. I would say just start with Kleppner.

 

[Shivam3013]

Well, Morin uses quite a bit of calculus so Spivak would be good preparation in terms of the math. For the physics though, as aforementioned, it's probably better to go through a less rigorous book (but still excellent) such as K&K. But then, with the assumption that Morin is a very tough book, don't go through something like Walker, Serway or Halliday. Also, how are you finding Spivak so far? For most people, unless you have a very strong grounding in algebra and geometry, it's quite difficult. If it's a bit rough, then I would suggest going through Lang as an introduction, then a more rigorous treatment in Spivak or Apostle.

 

[tridianprime]

Well, previously I went through "calculus made easy" by Thompson and I'm doing fine so far. It's challenging no doubt but that just helps me improve. Thanks, resnick and Halliday does seem appropriate. I might start working through that now.

 

[tridianprime]

Edit: I meant K&K not R&H.

 

[Shivam3013]

Oh, if you went through Thompson's book then there is no need to go through Lang. With spivak and others, its best to have a bit of a calculus background beforehand, which you do. Also, I think Halliday is not a very good book. For starting out, you can and should go with K&K and then move to something like Morin.

Edit: Oh, nevermind then.

 

[tridianprime]

I hear courant is good for applications so would you suggest I do that after spivak so that I have a pure and applied approach or is it not worth it?

 

[Shivam3013]

Courant is a great book and it does have many applications to physics. After spivak, you can go with apostle or courant to get a more rigorous background. It will be mostly review, but you will learn quite a bit. I say if you have the time, definitely go through them.

 

[Student100]

I guess I'm the only one who actually likes Resnick and Halliday. The problem sets are nice, and the layout is good for use later as a reference. I actually have the FoP version with Walker and just bought the Physics version with Krane to compare them.

 

[tridianprime]

I will, thanks.

 

[Shivam3013]

Student100, it just seems like a pretty bad book. Really, it's decent but the other better books make it look terrible. Tridian, you're welcome.

 

[jesse73]

Just a suggestion but you should go to the local college or university library and look at the many books on classical mechanics or intro physics and read a chapter see how the authors tone speaks to you and how the mathematical level compares to your own. Try a problem or two and look if it has access to some solutions if you are self studying. You will know which book is actually helpful to yourself not some other person.

Asking for recommendations on the internet tends to turn into competitions of who started physics with the most advanced book (Goldstein and Jackson here. joking). You need advice tailored towards your level.

 

[Shivam3013]

Jesse, the thing is, most books are just obviously good or bad. For the most part, with some exceptions, majority of people will agree whether a book is good or not. It's better to ask for recommendations by people who have read such books in detail (on a forum, the professors etc) then to read a chapter and trust your own judgement.

 

[Student100]

Student100, it just seems like a pretty bad book. Really, it's decent but the other better books make it look terrible. Tridian, you're welcome.

I've also got K&K, but haven't had a chance to go through it at all. I guess maybe my take to it might change, but it seemed like a well laid out book.

 

[Shivam3013]

Kleppner and kolenkow's book is an excellent textbook for introduction to classical mechanics. But that doesn't mean you only read the good books. Whenever I had time, I just read a textbook which wasn't specifically recommended to me. And really, even after something like K&K, you can learn a lot from H&R.

 

[jesse73]

Jesse, the thing is, most books are just obviously good or bad. For the most part, with some exceptions, majority of people will agree whether a book is good or not. It's better to ask for recommendations by people who have read such books in detail (on a forum, the professors etc) then to read a chapter and trust your own judgement.

It is subjective and dependent on the level of the student. Some books are better when you know the material and some books are better when you are learning the material. This usually causes problems for professors picking books who sometimes choose books based on their own preferences as masters of the material not learners.

This is why it is usually better for the student to determine what book speaks to his level and learning style unless a book is just factually wrong but you would be hard pressed to find a book in the library that is factually wrong but he could look up reviews for the book to determine if there are factual inaccuracies in the book.

Buying or loaning a book isn't a life decision that you have to stand by. You could choose a book to learn the basics of subject than choose a different book to keep for reviewing or to mastering the subject.

The process of learning physics is the process of refining your sophistication which is why everyone doesn't start with Jackson to learn E and M.

 

[WannabeNewton]

Kleppner is a perfect first mechanics book as long as one is dedicated to the text and willing to struggle if struggle presents itself. It is used ubiquitously in honors intro mechanics classes across the US. Hell it's the only intro mechanics book I've come across that actually states Newton's 1st law correctly so it should be used simply for that!