Will linear algebra help me in more advanced diff eqs study?

[kostoglotov]

I just finished up Stewart's Calculus Textbook, and the last section was on solving 2nd Order Non-Homogeneous Diff Eqs using power series.

I've looked through Paul's Calculus page in the Differential Sections, and can see that there is still a lot more beyond Stewart's that I'd like to study; Fourier, Laplace, PDE's, systems of DE's, higher order DE's.

I also however wanted to do the MIT opencourseware course on Linear Algebra after finishing Stewart's Calculus. From what I've perused, I get the impression that actually doing the more advanced Differential Equations stuff after completing Linear Algebra might be the best way to go anyway. It seems like the more advanced stuff in Paul's Calculus that wasn't covered in Stewart's involves many concepts from Linear Algebra anyway, and the Linear Algebra course seems to cover some Differential Equations stuff.

Are my impressions correct? Or is this just some superficial overlap?

 

[HOI]

Certainly much of "elementary" differential equation is linear differential equations, the theory of which is basically Linear Algebra. And many techniques for solving non-linear equations involve solving linear equations to start with.

 

[artfullounger]

According to my ODE lecturer back when I was doing maths, there are some significant and non-trivial links between the subjects. However we didn't really go into it since it was a more computationally oriented course, just leaving it as a section that we could look through "for culture" until we finished LA2.

That said certainly some computational aspects will come in, e.g. solving some linear systems and also using Wronskians in the variation of parameters method (which I totally fail to recall anything about other than it involving some determinants and the name "Wronskian" xD )

 

[Kilgour22]

I got a C- in Linear Algebra, then the following semester I got an A+ in Differential Equations. Although Linear Algebra was a prerequisite for DE, I found it mostly useless except for the odd appearance of linear independence, Cramer's Rule and determinants (Wronskian). I can't comment on PDE's, however; perhaps having a solid understanding of eigenvalues and eigenvectors will help though.

 

[CivilSigma]

Same here, Linear Algebra was a prerequisite for my ODE class, but my professor only used it to explain theory and not the ODE themselves.