Second Course in Linear Algebra

[Porthos]

I am planning my courses for next semester, and I am unsure of which direction to go in with linear algebra. I have already taken the following course:

Linear Algebra I
Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.

The course went well, and I am looking forward to a second course, but my hope is to eventually do graduate work in physics or math, probably on the more theoretical side of physics, but I am only in my first year, so I am not entirely sure at this stage. I have the option of taking either one of the following courses:

Linear Algebra II
Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.

OR

Intermediate Linear Algebra
A rigorous development of lines and planes in Rn; linear transformations and abstract vector spaces. Determinants and an introduction to diagonalization and its applications including the characteristic polynomials, eigenvalues and eigenvectors.

The former is offered through the Applied Mathematics Department and the latter is through the Mathematics Department. Neither one is an anti-requisite for the other. The only significant difference, besides the department offering the course, is the fact that the former requires a second course in calculus. My plan is to only take one of the courses, and I am taking the second course in calculus in the coming semester, so I cannot take the former in the coming semester. If, however, it is the better course for what I am looking for, I am fine with waiting.

Basically, I am wondering which one people think will be more useful for physics? I recognize that you have not (necessarily) taken either course, but I would imagine that those with a greater knowledge of advanced physics than I have would have a better idea than I do of which one seems to be of more direct use. I assume it is the former, seeing as it is more based on the applications of linear algebra, but I wonder if it would be of more use to go more deeply into the theoretical aspects of linear algebra in order to be better prepared for potential graduate work?

I have spoken to my physics professor this semester, and I got the impression that he doesn't feel that it matters which one I take (neither is actually a requirement for physics), but I was curious as to what others with experience think about this.

This thread (https://www.physicsforums.com/threa...near-algebra-ii-or-numerical-analysis.563174/) specifically discusses Linear Algebra II at Western University (where I am located), but it is comparing a different course.

I appreciate any advice you can provide.

 

[jedishrfu]

My guess would be linear algebra 2 looks more like something a physics major would take. It has differential equations, oscillators...

 

[Mmm_Pasta]

Definitely Linear Algebra II - I've encountered nearly every topic in that description in physics.

 

[Porthos]

Thanks, jedishrfu and Mmm_Pasta. That is what I figured, but I thought that it wouldn't hurt to ask. I appreciate you both taking the time to respond.

 

[Matrix0]

I understand your dilemma in choosing between Linear Algebra II and Intermediate Linear Algebra for your second course in linear algebra. Both courses seem to cover important topics that could be useful for graduate work in physics or math. However, based on my experience, I would recommend taking Linear Algebra II.

Linear Algebra II seems to have a more applied approach, covering topics such as vector spaces, orthogonal sets, eigenvalue problems, and linear transformations. These are all important concepts in physics and could provide a more practical understanding of how linear algebra is used in real-world situations. Additionally, the course also covers applications such as coupled differential equations and image approximations, which could be beneficial for your future studies in physics.

On the other hand, Intermediate Linear Algebra appears to have a more theoretical focus, with a rigorous development of lines and planes in Rn and abstract vector spaces. While these are important concepts, they may not have as direct of an application in physics as the topics covered in Linear Algebra II.

Furthermore, the fact that Linear Algebra II requires a second course in calculus could also be an advantage. Calculus is a fundamental tool in physics, and having a deeper understanding of it could enhance your understanding of the applications of linear algebra in physics.

Ultimately, the decision is up to you and what you feel would be most beneficial for your future studies. However, based on the information provided, I believe that Linear Algebra II would be the more useful course for your goals in pursuing graduate work in physics or math. I wish you all the best in your studies.