log(xB)

If you get it, then you win 50 extra points which can be applied to a variety of flavored beverages.

The purpose of this post is the same as it was this time last semester: to get my notes for my math test tomorrow down somewhere, just to help me remember it. This will be the format for the notes

Section number- what knowledge can be acquired by learning the section

How to do it, in Brian terms.

Here is the breakdown by sections:

7.1 Transforming a second order differential into a system of first order differential equations

Set x₁ to u, aşa că u'= x'₁

Then set x₂ also to u', and then u''=x'₂

Get the original equation in terms of x₁ equal to x'₂

7.2 Verify that a given vector satisfies a given equation

Learn basic linear algebra

7.3 Determining linear relationships between vectors

Give all vectors a constant in an equation similar to

C₁x₁+C₂x₂+C₃x₃=0

Write as an augmented matrix

Solve and pray they are all different constants

Part II Finding eigenvalues and eigenvectors

...Find the eigenvalues.

...Find the eigenvectors

7.4 Finding the Wronskian of a given vector, finding the interval of linear independence, find a system of equations that verify linear independence

You're given x₁ and x₂ vectors

Find W, and where it is zero, those values don't exist. That means that the interval of linear independence is everywhere that those values aren't.

The system of equations that verify linear independence is found by simply finding a vector that satisfies x'=Px

7.5 Find the general solution of a given system with different, real eigenvalues

Find the eigenvalues(these will be known as r₁ and r₂), then the eigenvectors (represented by ξ₁ and ξ₂)

Your solution is of the form x=c₁ξ₁e^r₁t + c₂ξ₂e^r₂t

...Yeah, it is taking too long to do the html code on this, and I won't do it otherwise... so I won't do it any more.

Bombachus

• Bill Gates' Facebook
  

The person who realized you can pop corn deserves a Nobel Prize.