What level of mechanics should go for? | strategies for mastering problems?

[Alg0r1thm]

Hi everybody,
The question sounds dumb, but I asked it, probably someone had the same experience, and can help me or give advice on it about what I'm going to do next !
I know calculus until the double integrals and I don't know enough about Lagrange multipliers ( Indeed, looking for intuitive proof ) and also I'm looking for a way to get through mathematical Analysis, topology and stuff.
Well, I know the concepts, probably not skilled at solving all of the problems I know the techniques of, it is the matter of mastery not knowledge.
I'm going through a course in introductory linear algebra these days.( but no applications )
I have passed high school physics, but I have no information about modern physics, of course I know about the basic ideas stimulating the modern physics, however, I prefer to say I have no information about it.
I'm pretty confused by the variety of subjects available in hand, specially in the mathematics , I require lots of mathematical techniques to go through advanced subjects awaiting for me in physics.
I want someone to advice me and help me to clarify what I'm going to do next.
With all things mentioned above - what level of classical mechanics should I study?
What problem solving books do you recommend for the mastery of the subject?

Thanks

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[jfizzix]

If you're looking to get a Bachelor's in physics, you will almost certainly need to know the following math (with the understanding that you've mastered high school math):

(for freshman/sophomore mechanics,electromagnetism, thermodynamics)
-Differential and integral Calculus of one variable
-Multi-variable Calculus

(for upper level mechanics, electromagnetism, quantum mechanics, and statistical mechanics)
- Ordinary differential equations
- partial differential equations
- linear algebra
- vector calculus
- Complex analysis
- Probability theory and statistics (also indispensable for anything you do in the lab)

(for more advanced classes, the courses you need are particular to the subjects you're taking)
- Differential geometry for general relativity
- Group theory for particle physics

I only have a limited idea of exactly what is needed though. You may, however be interested in this book by Leonard Susskind:
The Theoretical Minimum: What You Need to Know to Start Doing Physics
I haven't read it, so you'll want to use your best judgement. It sounds much like what you might be looking for. Also, he has online lectures for free on YouTube about all sorts of topics in physics.

Hope this helps:)

 

[Alg0r1thm]

If you're looking to get a Bachelor's in physics, you will almost certainly need to know the following math (with the understanding that you've mastered high school math):

(for freshman/sophomore mechanics,electromagnetism, thermodynamics)
-Differential and integral Calculus of one variable
-Multi-variable Calculus

(for upper level mechanics, electromagnetism, quantum mechanics, and statistical mechanics)
- Ordinary differential equations
- partial differential equations
- linear algebra
- vector calculus
- Complex analysis
- Probability theory and statistics (also indispensable for anything you do in the lab)

(for more advanced classes, the courses you need are particular to the subjects you're taking)
- Differential geometry for general relativity
- Group theory for particle physics

I only have a limited idea of exactly what is needed though. You may, however be interested in this book by Leonard Susskind:
The Theoretical Minimum: What You Need to Know to Start Doing Physics
I haven't read it, so you'll want to use your best judgement. It sounds much like what you might be looking for. Also, he has online lectures for free on YouTube about all sorts of topics in physics.

Hope this helps:)

Do you have any strategy for following online video lectures?
I have found that video lectures without a textbook won't be any of use due to the fact that you have to review stuff formally and practice enough for the new concepts to sink in!

 

[jfizzix]

The great thing about video lectures is that the instant something new comes up that you're not familiar with, you can pause the lecture, and look up the topic online. Wikipedia is a surprisingly good resource for a lot of physics topics. Of course, the online course might have its own books to recommend (as in an official syllabus).

 

[Alg0r1thm]

The great thing about video lectures is that the instant something new comes up that you're not familiar with, you can pause the lecture, and look up the topic online. Wikipedia is a surprisingly good resource for a lot of physics topics. Of course, the online course might have its own books to recommend (as in an official syllabus).

Well, because of reading rudimentary stuff in classical mechanics for several times, I feel bad when I want to start a new book of classical mechanics, since most of the books should be read from the beginning ( due to their language and things they mention and build the next chapters upon it ), I personally, don't learn or review topics with reading a book completely anymore, my question is, is this a bad habit that I have to get rid of? probably you have had same experience.
Most of the issues I'm dealing with these days are, for instance, I had covered some topics before starting a book on the subject, right now, when I face the topic I had read before, I feel tired on that chapter and I stuck, simply don't progress anymore, and most of the ideas will be repetitive for me.
I'm telling you my problem, and want to know your strategy, it may be possible that you've had the same experience.
Personally, I have found that, reading and covering a concept before dealing with it in a real course can have both advantages and disadvantages, and one of the disadvantages is, the concept seems boring and not fresh anymore.
You may accuse me to have lack of interest, but really not, I do like Physics, but it's stupid to review repetitively a topic that you had covered before.I hope I'm clear enough about the problem I've faced.

 

[jfizzix]

As far as course work in physics goes, I can only really speak from my own experience, and what works for me might not work for you. That being the case, my approach is as follows:

1.)I start with the homework/assigned problems
2.)I learn what concepts need to be learned to understand how the problems work and how to solve them
This I do by skimming the chapter or sections that have material about the problem (and the concepts behind them).
3.) With this model for how a particular problem works, I try to tie it to the fundamental concepts discussed in the course
That way, I have a better understanding of the concepts that could be used to solve problems I haven't seen before.
If the problems are well chosen, you can cover all the relevant material in a course.

I can't say that this method is easy, but it might be a useful alternative to trying to simply read the entire chapter from beginning to end.

 

[Alg0r1thm]

As far as course work in physics goes, I can only really speak from my own experience, and what works for me might not work for you. That being the case, my approach is as follows:

1.)I start with the homework/assigned problems
2.)I learn what concepts need to be learned to understand how the problems work and how to solve them
This I do by skimming the chapter or sections that have material about the problem (and the concepts behind them).
3.) With this model for how a particular problem works, I try to tie it to the fundamental concepts discussed in the course
That way, I have a better understanding of the concepts that could be used to solve problems I haven't seen before.
If the problems are well chosen, you can cover all the relevant material in a course.

I can't say that this method is easy, but it might be a useful alternative to trying to simply read the entire chapter from beginning to end.

Seems to be a good method, I have to test it, although I approximately a similar method.
However, if you could tell me a good book with well chosen problems for classical mechanics, I would appreciate you your help!

 

[jfizzix]

For introductory classical mechanics, there are many good introductory books

For intermediate classical mechanics, (dealing with Lagrangians and Hamiltonians and such) I like Thornton and Marion

For advanced (graduate level) classical mechanics, I like Goldstein.

That being said, I would just look at free online courses and see what materials they suggest. A lot of standard textbooks are quite expensive, though a good investment if you'll be using them as a reference as well.

 

[homeomorphic]

If you are an intuitive sort of thinker, don't even go near Thornton and Marion. Too formal. I'm not sure what to use for intermediate level classical mechanics, which is probably where you are at (maybe Susskind), but for advanced classical mechanics, because you seem keen on the math, I would definitely go with Mathematical Methods of Classical Mechanics, by V I Arnold.

 

[Alg0r1thm]

If you are an intuitive sort of thinker, don't even go near Thornton and Marion. Too formal. I'm not sure what to use for intermediate level classical mechanics, which is probably where you are at (maybe Susskind), but for advanced classical mechanics, because you seem keen on the math, I would definitely go with Mathematical Methods of Classical Mechanics, by V I Arnold.

Thank you for your recommendation of this bright book!
I didn't know this book, but I checked it right now and found it interesting.
It's really enjoyable to have different sources with different insights about the same topic!