What to review from linear algebra for a differential equations class?

[-Dragoon-]

I'm going to be taking a class in ordinary differential equations over the summer and have about 2 weeks to prepare. The class has linear algebra as a prerequisite, and I just wanted to know what I would need to review from linear algebra to prepare myself for the course?

 

[redrum419_7]

matrices

 

[micromass]

Depends on the course of course. But I think that review eigenvalues, diagonalization and the Jordan canonical form would be ideal.
Maybe you can even review the matrix exponential (or study it if you haven't seen it, it's not too hard).

 

[QuarkCharmer]

I just finished the course a week ago, you should review matrices a bit, but the real meat comes from eigenvalues as micromass put it. You need it to do systems of DE's. Check out pauls online math notes for systems of DE's to get the idea:
http://tutorial.math.lamar.edu/Classes/DE/RealEigenvalues.aspx

 

[mathwonk]

the absolutely basic stuff to review is bases, and the fact that the general solution to a linear equation of form Lx = y, is formed from a particular solution plus a general solution of the corresponding homogeneous equation Lx = 0.

 

[-Dragoon-]

So just matrix algebra and eigenvalues/eigenvectors would suffice? What about things like vector spaces, subspaces, spanning sets, and bases? Or linear transformations/mappings and determinants?

Also, I didn't cover canonical transformations which is covered in the linear algebra II class that I haven't taken yet.

 

[20Tauri]

I'm taking Differential Equations now. At my school, LA is just suggested, not required, for DE, but we have definitely run into LA concepts such as determinants of matrices, linear independence, bases of functions, etc.