Progression in Mathematics for Physics

[KUH96]

Hello all, this is my first post. Any help will by greatly appreciated!

I just started reading a degree in physics at imperial college. I just want to ask how should I progress through the mathematics for physics. I've worked through Mary Boas' book from chapter 1 to 8. Is it a good time now to start Complex Analysis, PDE or Tensor Analysis? What other topic should I also try to learn? Thanks.

 

[ShayanJ]

Its a very good start to learn the materials covered in that book. If you do it well, you probably won't need anything else from mathematics for the rest of your study in college. But if you want to go further, you'll need much more math!
And about the question that is it a good time to learn them or not! well, you're going to have a course on these things later. You can wait for that course but that won't cover all of it, but only a selection of subjects that will certainly miss some important ones. If you study now, you'll have an easier time in that course and also can learn deeper than others. Also you can cover more.
I strongly suggest you to learn calculus of variations, vector and tensor analysis, complex analysis, Sturm-Liouville theory, matrices and determinants, curvilinear coordinates, some special functions, and at least some introductory knowledge about linear algebra.
Just take it easy. You don't have to do it in one week, or even one month. You can move very very slowly.

EDIT:
Now that I look at that book, it seems to be good that you have Arfken's only as a back up.

 

[KUH96]

Now that I look at that book, it seems to be good that you have Arfken's only as a back up.

What do you mean?

 

[ShayanJ]

What do you mean?

Boas's book has a lower level than Arfken's and so tries to make things a little easier. For example she doesn't cover Sturm-Liuoville theory explicitly! which Arfken does and its good to learn the theory the way it is. There may be other things too so my suggestion is, you read Boas's book and after finishing it, you can check Arfken's and read the parts that Boas missed or explained not as good. Also reading Arfken's after actually knowing something about the subject, sometimes deepens your understanding.

 

[Matrix0]

Hello and welcome to the world of physics! It's great to hear that you are already diving into the mathematics for physics. In my opinion, there is no one "right" way to progress through mathematics for physics, as it will depend on your individual learning style and goals. However, I can offer some general advice.

Firstly, it's great that you have already worked through Mary Boas' book. This book covers a lot of important mathematical concepts that are essential for physics, so you are off to a good start. As for whether it's a good time to start Complex Analysis, PDE, or Tensor Analysis, it really depends on your current level of understanding and comfort with mathematical concepts. If you feel confident in your understanding of the material covered in Boas' book, then it may be a good time to move on to more advanced topics. However, if you feel like you need more practice and reinforcement of the concepts covered in Boas' book, then it may be beneficial to spend more time on those before moving on.

In terms of other topics to learn, there are many mathematical concepts that are important for physics. Some suggestions could be linear algebra, calculus (including multivariable and vector calculus), differential equations, and probability and statistics. It's also important to have a strong understanding of basic algebra and trigonometry, as these are the building blocks for more advanced mathematical concepts.

Ultimately, the key is to find a balance between challenging yourself with new concepts and ensuring a solid understanding of the fundamentals. Don't be afraid to ask for help or seek out additional resources if you feel stuck or need more practice. Good luck on your mathematical journey in physics!