Which Math Course is More Essential for a Physics Major?

[jbrussell93]

Matrix Theory. 3 Credits.
Basic properties of matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and Jordan normal forms. Introduction to writing proofs.

Applied Analysis. 3 Credits.
Solution of the standard partial differential equations (wave, heat, Laplace's eq.) by separation of variables and transform methods; including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics.
I've taken the standard calc, ODE, statistics, and mathematical methods. I haven't had a formal linear algebra course though I've gotten some exposure in my other courses. I've had little exposure to solving PDEs so I'm leaning towards applied analysis. What do you guys think is the more essential math course for a physics major?

 

[ZapperZ]

What exactly did you do in your "mathematical methods" course? Shouldn't you have covered linear algebra/matrices and special functions in such a course?

Zz.

 

[SteamKing]

I think you'll have to bite the bullet and take both courses eventually.

 

[jbrussell93]

What exactly did you do in your "mathematical methods" course? Shouldn't you have covered linear algebra/matrices and special functions in such a course?

Zz.

Complex analysis, ODE review, Fourier transforms/series, vector analysis, and some tensor analysis. We did not cover special functions. We covered eigen value problems related to diagnalizing matrices but not much outside of that. I feel like I got a bit gyped in that class actually...

 

[Matrix0]

I would highly recommend taking both the Math elective for physics on Matrix Theory and the Applied Analysis course. Both of these courses cover important mathematical concepts and techniques that are essential for a physics major.

The Matrix Theory course will provide you with a strong foundation in linear algebra, which is crucial for understanding many advanced topics in physics such as quantum mechanics and electromagnetism. The course will cover topics such as determinants, vector spaces, and linear transformations, which are fundamental concepts in modern physics. Additionally, the course will introduce you to writing proofs, which is an important skill in the scientific community.

The Applied Analysis course will focus on solving partial differential equations, which are widely used in many areas of physics. This course will teach you important techniques such as separation of variables and transform methods, which are essential for solving PDEs in physics. Moreover, the course will cover topics such as Fourier and Laplace transforms, which are powerful tools for analyzing physical systems.

Overall, both of these courses are highly relevant and essential for a physics major. I would recommend taking both if possible, as they will provide you with a strong mathematical background that will be valuable in your future studies and research in physics.