noleguy33

@TomServo

Absolutely.

I definitely think differential equations is extremely valuable and has many uses throughout engineering. I look back on the course, and what I took from it was 5-6 techniques used to solve differential equations and ~1-2 lectures on how to set up differential equations The lectures on how to set up differential equations were tank problems, decay problems, spring problems, circuit problems etc. I'm sure they are similar in each course. I found that section to be helpful, taking real world applications and modeling the behavior using differential equations. The 5-6 techniques we learned to solve them, however, seemed to be a bit limited. In talking to the professor, I was told those techniques would only solve ~2% of the possible differential equations we might see. Now, my teacher might have been way off with that estimate, I just haven't seen anything to the contrary. So basically I feel like I took a class with 2 useful lectures, and the rest was preparation to solve 2% of the possible problems we might see. I just found that a bit bizarre. Computers will be used to solve the rest.

Now, the same could be said about integration, and that computers can be used to solve most integrals. But I have found, in most of my applications, the integration techniques I learn cover 95% of integrals I have seen. For me, it was a useful course.

TomServo

That may be because individual, non-math classes will discuss how to solve those differential equations. A lot of physics/engineering courses will make time to talk about how to solve the relevant equations for the class. In fact it may even become a primary focus of the class. Many classes that are nominally physics or engineering classes are in fact math classes.

Personally I think diffy qs and linear algebra should be combined into the same class, everywhere. I think my math education was compromised by *not* being able to study systems of differential equations with matrices.

NeoDymium

Nah, DiffEqs is obnoxious to learn as it is. Don't need to combine them with tedious LinAlg.
If you haven't had your fill (or just plain need them), take PDEs. Those use concepts from both ODE and LinAlg.

noleguy33

If individual non-math classes go over how to solve specific DE's, why do I need to take an entire class devoted to solving them?

noimagination

That's how it works at my school.

GLOBALTRAVELER

That was always a "head-scratcher" for me. Why was my school telling us to take Linear Algebra AFTER Diff Equs but wanted to give a 1 or 2 lecture "fast intro" of Linear Algebra during the Diff Eqs course??

NeoDymium

LinAlg does make sense before DiffEqs. It's easier and you actually apply concepts such as the Wronskian/eigenvalues which are better covered in LinAlg than in DiffEqs that would be helpful to know better for DiffEqs.

sumzup

In my school, there's a 3-quarter sequence: 1) Differential Equations, 2) Linear Algebra, and then 3) Let's use them together!.

AncientGammoner

I took a single 5 semester unit course in combined linear algebra/differential equations. It wasn't bad learning them together since the LA stuff you use to solve DE.

NeoDymium

LinAlg->DiffEqs->PDEs would make the most sense.

TomServo

I'm not saying linear algebra is hard to understand without diffy qs, but I'm saying that systems of coupled diffy qs are something you can't even cover in your diffy q class *unless* they either made linear algebra a prereq or combined diffy qs and linear algebra into one class. Fortunately my physics program has combined relativity/mathematical methods class at the end of the intermediate classical mechanics series to prep you for E&M and quantum, but I wonder what other schools do.

Anyway, they are about to switch to a combined linear algebra/diffy q class, so you can cover systems of diffy qs, which is how it ought to be done. Now here's a thought: a year-long linear algebra/diffy q/complex analysis sequence.

yagottabelieve

When I was an undergrad, the diff eq class I took also covered a fair amount of linear algebra. There were also other linear algebra courses one could take that went into more depth. (All of these classes were offered by the math department.) Except for a class that was on the theoretical math track, the most advanced prerequisite was multivariable calculus.