Question

Differential equations - if you have a differential equation like y'' -2y'+2y=x, or something like that, what does it have to do with the solution of the corresponding polynomial?

Answer 1

what is "it" ?

Answer 2

...I don't think I understand your Q

Answer 3

i mean, it as in solution to differential equation. also, i'm just curious; just neefd a very very basic ubderstanding

Answer 4

we assume there is a solution; and try to define a function that works in generality

Answer 5

the details elude me; but e^r seems to be the best fit for these

Answer 6

e^rx that as

Answer 7

HOw would go go about solving y'+2y''+1=e?

Answer 8

is that a typo?

Answer 9

easy second-order homogeneous eqn if not

Answer 10

y = yh + yp

Answer 11

assume e^rx is a solution to the homogenous part:

y = e^rx
y'= r e^rx
y'' = r^2 r^rx

y'' -2y' + 0y = 0

r^2 e^rx -2r e^rx +0 e^rx = 0
e^rx (r^2 -2r) = 0 ; when the poly goes zero

Answer 12

r = 0 and r = 2

Answer 13

Ok, if I don't understand the assume e^(rx) is a solution ot he homogenous part, should I leave?

Answer 14

yh = a e^0x + b e^2x

Answer 15

lol, maybe :)

the question assumes you know some baser things

Answer 16

Ok, if I want to learn, what are baser things?

Answer 17

also, what are the prerequisites of baser things?

Answer 18

@inkyvoyd if you never heard of the characteristic polynomial or the stuff amistre is talking about I think you should start from the basics
http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Answer 19

yeah, pauls online is good stuff

Answer 20

Well, my 80's textbook on calc talks about it, and I was curious about the topic.

Answer 21

i think the proofing comes from real analysis stuff

Answer 22

prerequisites include:
calculus I-III
linear algebra (not strictly necessary, but I recommend it before learning DE's)

Answer 23

I have many holes in my calculus foundation, but I am really moreinterested in concepts that in a completely solid understanding, because I will eventually take calculus; right now I am just self studying

Answer 24

My txtbook is supposed to be calc 1-3?

Answer 25

And, linear algebra? Can I take that in parallel with calc?

Answer 26

calculus is definitely before DE's
you need a very solid calculus foundation before embarking on your study f DE's

Answer 27

(I know my comment about holes makes me sound like an idiot, and maybe I am, but I want to learn some of these harder things, because they interest me)

Answer 28

study of*

Answer 29

the best thing to do is to study up your foundational stuff in calc 1 thru 3 to have a foothold on whats going on in diffyQs

i learned it up the same way

Answer 30

Oh, I know what I"m missing. I'm missing partial differentiation. Sorry.

Answer 31

do you know integration by parts?
or trigonometric substitution integrals?

Answer 32

I understand both.

Answer 33

integration is the simplest diffyQ stuff that I know of

Answer 34

Won't say I would pass a test on them because I am very slow at calc (integration especially)

Answer 35

But I understand what they are

Answer 36

I'm not interested in being able to solve all of a certain type of differential equation, I just am curious about what's in the future for me.

Answer 37

ok well then I suppose you could try your hand at DE's
but that integration stuff is considered basic by the time you get to DE's, so you better practice that stuff 'till you can do it easily
there are no shortcuts in math, unfortunately

Answer 38

So far my motivation to learn about math is pushed by my interest in complex numbers, but I'm sure it won't last until I actually get to learn about them (Complex analysis?)

Answer 39

So, I should be able to understand the link given to me?

Answer 40

(A basic understanding)

Answer 41

not sure
look at the whole page
Paul's stuff goes from college algebra up through DE's
so if you are confused, go back a few sections
there is also a little section on complex numbers in one of the appendices

Answer 42

http://tutorial.math.lamar.edu/Extras/ComplexPrimer/ComplexNumbers.aspx

Answer 43

Thanks!

Answer 44

Sigh, I've been wondering about the applications of imaginary and complex numbers for a while now, and the closest I've gotten to even touching them is elecricity. My curiousity arose when I first learned about them and they were called "imaginary". Most people forget about them because they are completely "useless", but every textbook i've read say they have uses. Attempts to fin the applications led to hard math, and, the only thing I've learned about imaginary numbers that I can be proud of is euler's identity.

Answer 45

@TuringTest , scanned that page, and I think that's about as much as I need to know. I do realize that the people who developed solutions of differential equations were very good at calculus. :S Still though, I did understand what it was talking about for linear differntial equations, so I'll read on. Thanks again!

Answer 46

very welcome :)
be sure to thank Paul too, his notes are awesome !