Differential Equations or Matrix Algebra for Physic Major

[Thadis]

I am signing up for my third quarter of college classes soon and I have to choose if I am going to take Differential Equations or Matrix Algebra this quarter. I am given the option to take either of them and I do not know if I will be able to take the other one anytime soon. Which of the two classes would be the wiser choice take earlier for a Physics major?

 

[sabq]

Quite honestly, you will need both! and beyond! I took them together. In my opinion, it does not matter which one you take first, but just for the sake of an answer, choose linear algebra first.

 

[Thadis]

I hope I will be able to take both as I always hear people talk about how useful they both are. Though do you mind going into more detail of why you think I should pick Matrix Algebra first?

 

[TomServo]

An ideal situation would be to take a class that teaches both concepts together. BUT THAT IS RARE. I took diffy qs and linear algebra and probably the most "dropable" in hindsight would have been diffy qs, but this is kind of like saying which limb is easiest to cut off. Both classes are necessary, but for solving diffy qs in physics, they often teach these methods on the fly in the physics classes. For me it is recap, instead of brand new.

But if I chose which thing I'd rather have to learn on the fly WHILE LEARNING new physics at the same time, I'd choose diffy qs, maybe because linear algebra is less intuitive and less forgiving and quantum mechanics is hard enough without having taken linear algebra.

If you want to major in physics I consider linear algebra a must, I don't care what other "methods of mathematical physics" or whatever classes you may take. Linear algebra is unskippable because you don't want to go into QM with a shaky understanding of matrices.

 

[Thadis]

Ok thanks, I think I am going to try to get into a Matrix Algebra class then for this quarter. If I end up needing to I can take Diff Eq next year as I am a quarter ahead in math though I would prefer to stay ahead if possible.

 

[Vanadium 50]

If you are getting a physics degree at a place that does not require differential equations, transfer.

Seriously.

 

[atyy]

Is matrix algebra the same as linear algebra?

Linear algebra is important, but also applies to differential equations. For example, the Schroedinger equation in quantum mechanics is a dfferential equation. Yet linear algebra is the underlying mathematical structure of quantum mechanics.

What is most important is exposure to the abstract structure in linear algebra. A matrix algebra class, if it does not teach that, is not so useful for physics.

A differential equations class, OTOH, will teach some matrix algebra automatically, eigenvectors etc, and if taught with physics in mind, will teach linear algebra.

For example, http://www.pearsonhighered.com/educ...uations-and-Linear-Algebra/9780136054252.page is a differential equations text but includes linear algebra.

 

[Thadis]

Here is the descrpition of Matrix Algebra with Applications.

"Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences."

There is also a second class "Linear Analysis" which takes Matrix Algebra and Diff Eq. as a prereq.

 

[atyy]

Here is the descrpition of Matrix Algebra with Applications.

"Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences."

There is also a second class "Linear Analysis" which takes Matrix Algebra and Diff Eq. as a prereq.

The key thing needed for QM is the abstract vector space concept, which is listed in the course description.

You will probably also find matrices, eigenvalues, eigenvectors also taught in the differential equations course, because they are used to solve linear differential equations. Before QM I had taken a de class, but not a linear algebra class (which I still have not taken). However, I had learned the essential bits of linear algebra on my own from Seymour Lipschutz's "Linear Algebra".