Relationship between maths and physics

domwatts23

domwatts23

Jedi
I am wondering if anybody can help me; hopefully this topic may help inform others also.

In my school days I was relatively gifted at maths (nothing special) and I did enjoy it. I enjoyed other subjects more, however, and pursued philosophy for my degree.

Now I am trying to get myself up to a level in maths and physics from where I can try to understand some of the more difficult concepts and the maths.

The approach I have been considering is just to work my way up in terms of maths so I can start to get to University level. In terms of physics I have bought one or two 'popular science' books which were rated very highly just so that I can start to have a background into some of the topics (.e. relativity).

I wondered if anyone can give me some advice regarding whether this is a good route to go down or if there may be a more fruitful avenue to go down in terms of really developing my understanding of the subjects.

Also, I am particularly interested in understanding how maths relates to physics, so might anyone recommend me a good way to start understanding this also?

Thanks in advance.
 
Hello domwatts23,
I'm not sure to understand exactly, but do you want to study physics?
I would suggest to begin from the beginning: classical dynamics, Lagrangian and Hamiltonian formalisms, electrodynamics, special relativity, etc. Every step helps to understand better the next step, as in mathematics. I don't know what good books exist today, but I think that the Landau-Lifshitz books are good to start with. Maybe others would have other suggestions. There are also R. Feynman lectures that can be used as a complement to Landau's series. But I'm talking here about very old books, there may be other books today that are more interesting :)
 
Thanks for your quick reply! Yes I do want to study Physics, I also want to study Maths. I will look into what you have suggested, thanks again.
 
There are many books written for the educated general public that can be helpful. Like everything, there are things to know about what to question in what you read, and you may find some help with that here.

I read a lot of these books, mostly in audiobook form. The repetition helps with things I don't understand readily, and the different points of view help bring out the errors and biases that are inevitably present. One of my recent favorites was The Trouble With Physics by Lee Smolin. Another that I quite liked was The Clockwork Universe by Edward Dolnick. I could go on and on with titles.
 
Just to add to the other responses in cultivating your physics and math understanding, I have found that the _www.khanacademy.com website really helps with tutorials and videos that could possibly aid in starting from the very beginning of both of those fields.
 
I second that recommendation for the Khan Academy. You'll also (at least) want a textbook on mathematical methods applied to the physical sciences; Mary L Boas' is a classic.
 
This might be a bit of sideline for you. For studying Mathematics and Physics i.e. working through the equations and formulas I would recomend the computer software called MAPLE.
A bit of history. I work as an engineer. About a year ago I stuck my nose into a problem a work that was a bit outside may area. As its a small company that's ok. The problem was solving the forward kinematics of a Stewart Gough platform (flight simulator base). I left colllege in the early eighties and haven`t done much advanced maths or programming since then. I found out that the mathematics of these systems need to be solved using whats called symbolic manupilators.So I bought a home user license for Maple (about £200)
See http://www.facebook.com/Maplesoft. In the Uk I bought it from AdeptScientific.

This program has loads of student tutorials Calculus Matrices Ploynomials Prysics topics etc etc There is also a forum MaplePrimes which is good for help.
I'm no programmer ( when I did BASIC programming, used a Sinclair spectrum ) but was able to learn to use this and apply it to the papers I was trying to interpret on the problem.
 
If you want to look at a math book and your algebra and trig are up to speed, I must suggest this one:

http://www.amazon.com/Introduction-Calculus-Analysis-Volume-I/dp/1461389577/ref=pd_sim_b_2

Really awesome in my opinion... Calculus and all that is presented in a way that prepares you for future subjects. A lot of applications to physics are shown in appendices to the relevant chapters or in special chapters of their own. There is a picture here and there when it helps. The explanations are good. The pedagogical development is beautiful in a way modern intro textbooks just don't have for whatever reason.

I personally like to see math and play with it before I see it in a physics course except for those rare occasions where there is a professor who does more than just say, "Okay... Here is the equation for this situation." If you have a similar personality, because there are many people who can focus on the physics and not get too hung up on where the math comes from, then you should get through the integral and differential calculus sections of this book before doing too much physics. otherwise, you get the constant feeling of "Wait... Where did that come from?"

You could probably work the two concurrently somehow, but I would not be sure of the most efficient way to do that.

Ohh... If it interests you, this book above, note that in the Amazon customer comments someone mentions the name of an old book by another author that is the solutions to the exercises. Good luck finding it though... If you do, let me know, and I will buy a copy from you (it's out of print) :P

If you find you have the time for all this, here is an interesting online book that would interesting later on but not too later on:

http://www.math.oregonstate.edu/BridgeBook/toc/start

It approaches some basic topics from the standpoint of bridging the gap between math classes and physics classes

Oh and these:

http://www.amazon.com/Students-Guide-Maxwells-Equations/dp/0521701473/ref=sr_1_1?s=books&ie=UTF8&qid=1357598979&sr=1-1&keywords=students+guide+maxwells+equations

http://www.amazon.com/Students-Guide-Vectors-Tensors/dp/0521171903/ref=sr_1_2?s=books&ie=UTF8&qid=1357598979&sr=1-2&keywords=students+guide+maxwells+equations

Also nice books bridging the gap between math, the geometry it encodes, and thus why we use it in basic physics.
 
Thanks Ronan and Patience. I don't have enough money to be able to afford Maple yet, but once I'm definitely up to speed properly with algebra and trig I will look into the books you suggested Patience.

Thanks again.
 
Schaum's Outlines are also very good resources, they do math as well as physics, for high-school up to college level.
 
Hi Domwatts23

I have an honours degree in physics and a master's in electron microscopy but I always struggled with the maths side of the subject! What helped me was remembering that the maths is only a tool for explaining the physical theories and concepts. So I always had to relate every equation back to the physical idea that it was trying to represent. For example, as you know lots of physics is heavily dependant on differential calculus. On its own, a weighty differential equation scares the pants off me, but then I force myself to remember that it represents something real i.e. the rate of change of one quantity with respect to another. So, acceleration is the rate of change of velocity with respect to time, which is why it can be represented as a differential equation.

I found that by always forcing myself to think about the real physical ideas behind the maths helped quite a bit. Unfortunately, some lecturers and textbooks just concentrated on the maths rather than what it represented, and I always came unstuck in those classes. I failed my astrophysics final exam for that very reason - I didn't understand what the maths represented!
 
Thanks again for all the comments. I'm going to try to eventually go through all that has been listed!

ec1968 thanks for the tips, I think it will help me to remember what you have said as, from what I have heard, pure maths can be a bit of a rabbit hole for many people and bearing in mind what it relates to will always be useful for me.
 
I just finished exams on both courses in maths and physics, with the same motivation as you Domwatts23. A topic (I like to see maths and physics as one area syntheticly divorced from each other) which has always seemed very foggy to me which I think has much to do with missing fundamental or relational knowledge in teachers of (primary) schools. Anyways I set out to illuminate that fog, unwilling to accept the badges of logical dishonour I've early on been decorated with and integrated (almost 40 now).

The last half year (compressed express course) has been a real struggle, especially with differential calculus, trying to actually understand it, at it's most simple level. At oral exams I picked the most difficult differential calc. question and didn't pass, all the formulas of the discipline just floated around in my head and I almost couldn't answer a single question without my notes in hand. In physics I got the same topic, the exact one ec1968 describes above, here I could barely wiggle myself to a pass by describing the above.

Written maths and physics problems was much easier because you don't have to consider the meaning of it, you just apply pattern recognition and the right formula will somehow appear. But orally talking about math is super abstract imo and I obviosly hadn't understood anything. I was tricked by having put a lot of hours into it, succes in written assignments and had made a narrative that I understood the basics and by basics I mean the most essential, as in if you can't explain it to a child then you haven't understood it all.

Not saying this to discourage you, just a heads up on how the mind will deceive you for some peace of mind in that one is progressing. I'm thinking that my mind was protecting me from the pain of feeling like a blockhead by not understanding something which others easily gets. I should have done the feedback test; explaining to someone my understanding to see if I actually did understand anything by their approval. I'm doing the math course again, with the intent of applying that procedure and hopefully seeing the 'true face' of differential calculus.
 
Hi parallel,
Have you tried the (well known among students) Schaum's series on differential calculus? Maybe it could help :)
 
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