Relativistic Calculus Books & PDFs | Free Resources

[Somali_Physicist]

Just wanted any books / pdfs which introduce special relativistic calculus.

 

[Vanadium 50]

Calculus is calculus, and was invented centuries before Einstein. Special relativity largely uses only algebra - the transformations are algebraic, although one can set up a situation where the dynamics requires calculus: just as in Newtonian mechanics. So I don't know what you are asking. (Oh, and are you really a physicist?)

 

[Somali_Physicist]

Calculus is calculus, and was invented centuries before Einstein. Special relativity largely uses only algebra - the transformations are algebraic, although one can set up a situation where the dynamics requires calculus: just as in Newtonian mechanics. So I don't know what you are asking. (Oh, and are you really a physicist?)

I don't think I'm qualified to state I'm a physicist. I am an undergrad starting 2nd year, I was interested in calculus used in special relativity. I have read up on some questions using interesting derivates whilst answering said questions related to the time invariant.Also I think I should have said general relativistic calculus as I get your point on special relativity being mostly based on constant frames of references, which are often more conceptual than mathematically challenging.However i guess when you bring in vectorial problems you begin to use calculus often. Was looking for pdfs like that. I haven't started on general relativity but would appreciate an intro to it as well (Assuming there is a lot of calc. involved.

 

[Herman Trivilino]

Traditionally calculus is taught in a math department starting with a three-semester sequence of Cal I, Cal II, and Call III. Differential equations follows, although usually the prerequisite is only Cal II. You can polish that off with an undergrad course or two in differential geometry.

For an undergrad course in general relativity probably all of the above would be good to have, but usually they're not all required. The best strategy would be to ask the professors who teach the undergrad courses in relativity.

By the way, these professors are almost always happy to discuss these things with potential students. They are happy when students show an interest in the courses they teach. Unless you happen to approach them on a day when they're in a bad mood.

 

[Somali_Physicist]

Traditionally calculus is taught in a math department starting with a three-semester sequence of Cal I, Cal II, and Call III. Differential equations follows, although usually the prerequisite is only Cal II. You can polish that off with an undergrad course or two in differential geometry.

For an undergrad course in general relativity probably all of the above would be good to have, but usually they're not all required. The best strategy would be to ask the professors who teach the undergrad courses in relativity.

By the way, these professors are almost always happy to discuss these things with potential students. They are happy when students show an interest in the courses they teach. Unless you happen to approach them on a day when they're in a bad mood.

I have done a few calc units that weres required.I was thinking of going into pure maths electives as that is often more "creative" in mathematics.

 

[Daverz]

Just wanted any books / pdfs which introduce special relativistic calculus.

See here:

https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/

(Yes, I know, nothing to do with differential calculus.)

 

[Somali_Physicist]

See here:

https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/

(Yes, I know, nothing to do with differential calculus.)

thanks dude this is exactly the kind of stuff i was looking for.

 

[Vanadium 50]

this is exactly the kind of stuff i was looking for.

That's good. But it would help a lot if you were clearer about what you were looking for. As Daverz said, this has no relationship to what is usually meant by "calculus".

 

[bhobba]

Relativistic Calculus is just tensor calculus - but applied to Relativity

Here is a self contained account:
http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf

But you will learn it in any good book on SR and/or GR.

In order I would get - First for SR
https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

It emphasizes symmetry as the basis of SR - which IMHO is the correct approach.

For GR Dirac's little book explains the tensor calculus you need for that:
https://www.amazon.com/dp/069101146X/?tag=pfamazon01-20

Watch Dirac though - its brevity comes at a price - he just states the main result Ruv = 0 rather than motivates it - there are deeper reasons why it is so.

Also watch Tensor calculus in general - its a very brief and concise notation. Proving what look like simple things can be more difficult than you think. My vector calculus teacher at uni expressed it this way - don't pick up a book on tensor calculus for a bit of light reading - it will suck you in hours for hours.

Thanks
Bill

 

[Somali_Physicist]

Relativistic Calculus is just tensor calculus - but applied to Relativity

Here is a self contained account:
http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf

But you will learn it in any good book on SR and/or GR.

In order I would get - First for SR
https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

It emphasizes symmetry as the basis of SR - which IMHO is the correct approach.

For GR Dirac's little book explains the tensor calculus you need for that:
https://www.amazon.com/dp/069101146X/?tag=pfamazon01-20

Watch Dirac though - its brevity comes at a price - he just states the main result Ruv = 0 rather than motivates it - there are deeper reasons why it is so.

Also watch Tensor calculus in general - its a very brief and concise notation. Proving what look like simple things can be more difficult that you think. My vector calculus teacher at uni expressed it this way - don't pick up a book on tensor calculus for a bit of light reading - it will suck you in hours for hours.

Thanks
Bill

Awesome, I have pretty much developed a concise understanding of Special Relativity since I have done quiet a few units on it.However this year it will be further explained with hints of General relativity.I stumbled on tensors and was absolutely dumb founded , every day I find out I know less and less... and damnt it feels great!

 

[vanhees71]

Maybe also my SR introduction helps. It's, by the way not true, that SR consists only of linear algebra. The most important development of 19th-20th century physics is the development of the field concept by Faraday, brought into mathematical form by Maxwell, Heaviside, and the other "Maxwellians", and this is indeed vector and tensor calculus. In a sense it's "relativistic calculus", because it's tensor calculus in Minkowski space or, if you also include gravity and Einstein's General Relativity, a Lorentz manifold. So, here's my intro to SR (it's not finished yet, but maybe as an intro it's already helpful):

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[Somali_Physicist]

Awesome dude thanks a lot