Question

How do we rewrite 2nd order differential equation as system?

Answer 1

given a second order equation:
\[y^{\prime \prime}+ay^{\prime}+by=0\]make a new variable:\[z=y^\prime\]
solve for y'':
\[y''=-ay'-by=-az-by\]but y''=z', so our two equations are:\[z'=-az-by\]\[y'=z\]

Answer 2

Thanks , man

Answer 3

I learned about L U decomposition today

Answer 4

nice :) thats important.

Answer 5

hard to remember the elimination matrix though

Answer 6

ah, yeah, from a theory standpoint, its just important to know the L matrix is a record of your row reductions. actually being able to create the elimination matrix is more computational.

Answer 7

in my theory class last semester, we never had to create the matrix, we just needed properties.

Answer 8

do we learn about system of differential equation in this linear algebra class

Answer 9

my prof just lightly talked about it. It was in my graduate lvl differential equations class where were actually solved linear systems of diff equations.

Answer 10

because they are really useful for solving circuit analysis problems

Answer 11

so is it all graduate level classes for you now?

Answer 12

nah, im not going to take anymore. Unfortunately my school wont substitute them for classes i need to get my degree, so they count only as electives. I dont need anymore electives though =/

Answer 13

It's funny because I have classmate who is in opposite situation. Grad student taking undergraduate courses

Answer 14

ah yeah, i know a couple of grad students in the situation as well. i hope i dont have to do that >.< what classes are you getting ready for next semester?

Answer 15

linear algebra, circuit analysis, signal processing, and history

Answer 16

sounds awesome :) im taking complex variables (Zarkon has sold me on this idea), Modern Abstract Algebra, and two core classes (some polictics class and something else i dont care to remember lolol)

Answer 17

complex variables , same as analysis?

Answer 18

i believe so...im not too familiar so I dont know the detail, but one of my professors said it was pretty deep in analysis (which is a huge weakness of mine, unfortunately).

Answer 19

I heard my signal class deals with quite a bit complex numbers

Answer 20

Does signal proccessing have to do with Electrical Engineering? because EE almost wouldnt exist without complex numbers as well o.O

Answer 21

Yes, I am EE major

Answer 22

oh. my bad you probably told me that at some point >.< then yeah, complex numbers will be your best friends :)

Answer 23

I though I might learn linear algebra while I have time

Answer 24

do it!! its worth it. it has really far reaching applications. and it serves as a really good foundation. Other subjects become a lot easier to understand.

Answer 25

The first half of the grad differential equations course was linear systems, so I could pretty much do everything with knowledge about Linear Algebra. The second half involved analysis though, which killed me >.< lolol