[MA212/DE2] General Types of Mathematical Modeling in DE - Ch 2.9/11.3/11.4 (don't necessarily correspond, just examples)
Terms in this set (6)
Radioactive decay series equations
decay rate of nuclear species in this format X->Y->Z is described by:
dx/dt = -λ1*x
dy/dt = λ1*x-λ2*y
dz/dt = λ2*y
x'=αx(K-x), where K is the carrying capacity, and α is a constant
(by convention, I'm not using c and e for constants, because they don't distinguish integration constants etc for solving DEs and e is not the right constant to use, it's just any old constant, it can be *anything*)
x' = ax-bxy
y' = dxy-fy
x' = x(a-by)
y' = y(dx-f)
Example of one equation:
y'=y((3/4) - x - (1/2)*y)
one outgrows another at a specific point (value)
More information on the constants used in eqn etc (specific constants given on exam):
In the Logistic Growth Model, what does K stand for?
spring-mass-damper model with no gravity or other forces (note to self-to this def: revision might be needed)
my''+cy'+ky=0, assuming gravity is negligible.
You can solve this as a linear homogeneous DE by plugging in y'=w (1st equation) and solving for the jacobian matrix, etc.
spring-mass-damper model with gravity or other forces (note to self-to this def: revision might be needed)
my''+cy'+ky+f(t)=0, assuming f(t) describes the other forces like gravity or a magnetic force described by this function f(t).
You can solve this as a linear NONhomogeneous DE by plugging in y'=w (1st equation) and solving for the jacobian matrix, etc.
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[MA212/DE2] [REVISED] Phase Portrait Cases for _Linear/Autonomous_ systems of DEs (another method is to do trace/determinant, this is the eigenvalue/eigenvector way)
THIS SET IS OFTEN IN FOLDERS WITH...
Phase Portrait Reference Guide
Phase Portrait Eigenvalue Conditions
DE2 - Linear Algebra (Ch 8.1-8.3)
[MA212/DE2] Formulas to know for 1st exam