"methods of theoretical physics" vs "normal math classes"

marmot

Hey.

I am in a dilemma. Originally, I was gonna go the math minor route but I think I am deciding against it mainly because of the structure. I wanted to take an advanced calculus class to prepare myself for EM, but I really want to take an advanced forrmal logic class and that fills the place available for advanced calculus. There is a class called "methods of theoretical physics" which can count for my math reqs and the description is this:

"Mathematical methods applied to physical problems in mechanics, electromagnetism, and thermodynamics. Multiple integration, vector calculus, Fourier series, ordinary and partial differential equations, eigenvector problems, coordinate transformations, and complex analysis. Newtonian mechanics, rigid body dynamics, heat flow, electrostatics, harmonic motion, and waves."

Would this class be useful? Do I need to know mad vector calculus for electromagnetism or there are just some things that I need to dominate?

Dr Transport

A mathematical methods course is usually required for any degree program in physics and would be much more helpful than a logic course.

jtbell

You sure do! However, the vector calculus you get in a typical Calculus III course should be enough. Also, undergraduate E&M courses often spend a significant amount of time reviewing vector calculus. The first chapter of Griffiths (a popular E&M textbook) is devoted to vector calculus.

Disclaimers:

1. I assume you're in the USA.

2. I assume you're dealing with an intermediate / upper-level E&M course, not the second semester of freshman physics.

3. The situation can vary from one college / university to another. Check your course catalog for the official prerequisites for your E&M course.

marmot

i am sorry. what i meant is that if a mathematical method class would be enough for EM. i was taking before analysis, but i am gonna drop it for that class. i am not going to drop logic because its a class i wanted to take before forever and i am willing to make a lil sacrifice fr it.

ice109

you don't need advanced calc for em - you need vector calc.

why are you taking advanced formal logic? that will help you with nothing except logic - it won't even help you write mathematical proofs.

jtbell

At most colleges and universities in the US, you don't even need a mathematical methods class for an intermediate level E&M course. All you usually need is the vector calculus that you learn in (usually) in the third semester of a standard calculus sequence.

However, even in the US, there are probably exceptions to this. If you're at a university outside the US, then I would not want to give advice without seeing detailed descriptions of the E&M course and the math courses that you've already taken, and the mathematical methods course.

chwie

Well I did my major in math and physics and I can say that the methods course is enough for an introduction to electrodynamics, but I think that is better to do the minor in math, in the case of an Advance ED course it can be really helpful, because the real difference for example between of a intermediate course book and the Jackson is the math. Also the majority of the courses for methods in theoretical physic don't include modern methods like group theory and tensor. Group theory is important in QM, QF and depending of the approach for classical dynamics and ED. The tensor for GR, but for example the tensors are important in ED, because you can have all the Maxwell equations in one tensor equation, and also the multipole moments description should be more easy to understand too. my advices is that if you are interested in modern physics, is not enough with the calculus, DOE, DPE, Linear Algebra and complex analysis courses, you need group theory (abstract algebra) and tensor calculus or differential geometry, also maybe topology.

Also in physics some books use tricks that you will not understand unless you have a good background in analysis and logic. Also there are some tricks that are used in physics that any math can help you to understand, like the delta function that make a lot of sense in QM to help to the normalization of the improper vectors, but it is not well defined from the mathematical point of view.

Also the good part about taking the math course is that you learn the theory and it can be helpful to reduce problems with a lot of helpful theorems. For calculation, programs like mathematica and mathlab are better than any course.