1.1 Models/Direction Fields:
Find where y' = 0 , find where y' < 0 and where y' > 0
1.2 Integrating Factor:
Standard Form: y'+ p(t) y = g(t)
p(t )
u(t) = e
d
dt
u(t) y = u(t) g(t)
u(t) g(t)
y=
u(t)
3.1 Systems of Two Linear Algebraic Equations:
Finding Eigenvalues:
a11
a12
= det
a21
a22
= (a11 )(a22 ) (a21 )(a12 )
Factor to find 1 and/or 2
Finding Eigenvectors from :
!
(A i)x = 0
a11
a12
4.1 Intro to 2nd Order Linear Differential Equations
To determine linear/non-linear equation must be in this form:
y'+ p(t)y'+ q(t)y = g(t)
To determine homogeneous:
g(t) = 0
Force:
F = kx kL = mg
my'