So just completed my ODE course last Spring and, though I did well in the course, I am questioning whether I really learned anything.

Allow me to start off by stating that the scientist puts an intense emphasis on computation: tests include 5 free answer, drawn out issues without a partial credit. Very intensive; course averages are under departure but no curve.

I really don't know whether it is due to my prof or due to the character of the course, but solving ODEs feels just like fighter work. You are given a very special ODE, and you need to match this up to some very special algorithm and execute the computation. Great, after all that work I feel as that I will solve 0.5percent of ODEs now since the calculations are so technical. We have slightly deep into vector spaces, basis, etc. although the calculation was more extreme. Virtually all issues involved solving directly RREFs for matrices. The 3rd unit was more arbitrary. We spent a great deal of time utilizing the eigenvalue-eigenvector procedure to solve systems of differential equations. Yet more, quite computationally intensive. Consisted of solving long IBPs

At this time, I am about halfway through my Differential Equations course, which is based heavily on Linear Algebra. I have been enjoying the course and understanding all the stuff up until today, as Linear Algebra is becoming involved. I could only memorize outcomes in Alg, but I would rather not do so since I truly hate not knowing what I am doing. I have attempted to perform some Linear Algebra study in my own as a nutritional supplement, but it feels like that I essentially have to be aware of the whole class. At this time, it feels like I would just need to bite the bullet and then memorize since studying Linear Alg takes far too long from really doing DiffEq:-LRB-. I really do know the exact bare bones of Linear Algebra- matrices, matrix multiplication, RREF, a few things on inverses and linear transformations- however I was wondering if some of you guys knew of a great source that covers the minimum quantity of Linear Alg that a individual would have to understand for Diff Eq (transformations, foundations, inverses, eigenvectors, etc.). In the minimum, I'd love to know whether there is a course after DiffEq which revisits the substance of DiffEq in a way very similar to the way single-variable calculus revisits and reinforces the comprehension of previous substance. When there's such a course, I will feel a bit better about not entirely knowing what is happening at this time.

Problem Description: Require 3 rings, together with the next ring matching within the third and also the 1st within the second. Every one of these earrings has an arrow that could point north, east, west, west. If any ring is rotated clockwise our counter clockwise, then it'll rotate any adjoining ring at the opposite way.

When we take all 3 arrows to be pointing east, the number of moves does it take to make them point south and in what sequence should they be transferred?

Efforts so far: I have attempted to make three more vectors to represent the motion.

1 -1 0

-1 1 -1

0 -1 1

Where the very first row is the way the very first ring is changed and so on. However using this strategy only gives me a RREF that doesn't work.

0 -1 0

0 -1 0

1 0 0