Taking Honors Diff eq after shaky Calc III and Linear Alg courses

[stgermaine]

Hi. I took Calc III and Linear alg over the summer. The course was 6 weeks and we did not cover everything in each chapter. From Calc III, we didn't cover things like curl, divergence, and Green's Theorem. In Linear Algebra, we didn't do orthogonal functions, diagonalization, Eigenvectors, or Cramer's rule.

I'll be taking a honors diff eq class at my local community college (taking a medical leave of absence) and I'm afraid that having a rather shoddy base can screw me over later as I get into more advanced classes. I've just finished the courses, so I don't even want to look at numbers for a week or so, but should I review some of the topics I didn't get to cover at my summer school using the textbooks and MIT OCW?

Thanks!

 

[micromass]

Wow, I think you missed the most important stuff of calc III and Linear algebra. Now, this won't bother you in Diff eq (except perhaps the diagonalization), but it will become important in the long run. I suggest you self-study these topics as they are really important.

 

[MathWarrior]

I agree with micromass, you really missed a lot of material. In my Differential Equations class, we used eigenvectors like crazy, but that was more towards the end of the class. You can however take differential equations with only knowing calculus 2 in most cases.

What is your major exactly?

 

[stgermaine]

I'm beginning my third year and I started as a psych and econ major, but I decided to change econ to math.

 

[20Tauri]

My school required Calc III and suggested LA as prereqs for DE. I think the stuff your class left out of Calc III might be covered in a Vector Calc class, but I'm not sure. I wouldn't be worried about missing those topics for DE, but you're probably going to encounter eigenvectors and diagonalization in a DE course. You may be taught them as you go, though.

 

[deekin]

I'm glad somebody else asked this, as I'm facing a similar situation. I'm taking Applied Linear Algebra right now, and its looking like the prof will leave out eigenvectors, but will cover eigenvalues (so covering the first part of the chapter, but not the second part). Hopefully your LA class with provide you with enough to work with that studying on your own won't be too laborious.

 

[stf]

I'm glad somebody else asked this, as I'm facing a similar situation. I'm taking Applied Linear Algebra right now, and its looking like the prof will leave out eigenvectors, but will cover eigenvalues (so covering the first part of the chapter, but not the second part). Hopefully your LA class with provide you with enough to work with that studying on your own won't be too laborious.

Not really even sure how you could make sense of an eigenvalue without the eigenvector...

 

[deekin]

I have no idea, we haven't gotten there yet, so I don't know what either of them are. And it also turns out that I got it mixed up. Turns out we cover "Eigenvectors and Eigenvalues","The Characteristic Equation","Diagonalization" but he is leaving out "Eigenvectors and Linear Transformations" and "Complex Eigenvalues." Sorry, that was my fault for trying to explain from memory. I think I was just a little nervous about the prof leaving out some essential information from the course that I may need in later math and physics courses.

 

[Cuauhtemoc]

Eigenvectors and eigenvalues are important in Diff Eq, sure you can learn how to do it mechanically, but you are going to use it. In Boyce's book you start using them in the Fourier series chapter I think.