Should i be worried? (DE Course)

[Remixex]

Hello all, my question is if i should or not be worried about the apparent "missing" (or alternative) content about my DE course.
My DE course (and the only one in the list of courses i must take to get my degree) consisted on
First order ODEs (Separation of variables, homogeneous, Bernoulli's, etc) -> Applications (Newton's law of cooling, mixing problems, etc)-> "Superior" order ODEs (Oscillations, Euler's equation, variation of parameters, etc)-> Fourier Series (Coefficients, convergence, Parseval's identity)->Sturm Liouville problems -> Linear PDEs (Separation of variables, Source term, Wave equation, Laplace's equation, Heat equation, membrane problems)
Now onto the question at hand, we didn't see what most ODE specific courses do, system of ODEs and Laplace transform.
I'm aiming for a Geophysics degree and I'm finishing my second year, should i be worried about this missing content? Should i try to learn it by myself? Or is this course "good enough"?
Thanks beforehand

 

[S.G. Janssens]

"Superior" order ODEs

What are these? ODEs of order higher than one?

system of ODEs

If the answer to the question I asked above is "yes", then you will encounter systems of ODEs, because every ODE of order ##n## can be written as a system of ##n## (generally coupled) ODEs of order ##1##.

Laplace transform.

I would not worry too much about missing this in the course. It is very important for certain applications (e.g. in linear systems and control). If needed, you can easily pick up a book later on and learn it yourself.

should i be worried about this missing content? Should i try to learn it by myself? Or is this course "good enough"?

I don't think you should be worried, but I would perhaps consider taking a second course at some point during your student life. There are very interesting applications of (P)DE in geophysics that this course may not even touch upon, such as fluid flow or flow through porous media.

Incidentally, for a more qualitative, geometric view towards differential equations that connects well to current research and application, I could recommend the third edition of Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch, Smale and Devaney, 2012. The first edition is titled Differential Equations, Dynamical Systems and Linear Algebra by Hirsch and Smale, 1974. It is a beautiful book, accessible but a bit more mathematical than the subsequent editions.

It is my impression that some students are put off by a lot of initial courses on DE because they (still) focus on analytical solution techniques. If your course is like that, the geometric approach may provide some fresh motivation.

 

[Remixex]

Yes superior order is order higher than one but still ODEs (that's how we named it here), such as a 3rd order Euler's equation.
Thanks for the advice, the follow-up course of this (the one I'm taking and trying to finish right now) is called Oscillations and waves , which expanded on many of these concepts (the problem is no longer how to solve the differential equation, it is about actually writing it down interpreting the physical phenomena presented, and doing the correct approximations so an analytical solution is valid) , but the course is still analytical, numerical methods courses are a couple of semesters ahead.