MATH 2310 – DE Lecture 2
Standard first order linear model:
- A standard model for many first order linear initial value problems is:
dx
=kx , x ( t 0 )=x 0
dt
- This is a standard model for:
o Bacterial growth,
o Population growth,
o Radioactive decay,
o Warming and cooling,
o Mixing,
o Simple electric circuits,
o Etc.
Heating and cooling:
- IVP’s dealing with heating and cooling usually follow Newton’s law of cooling:
dT
=−k ( T −T ∞ )
dt
Electrical circuits:
- For resistors (unit = ohm [Ω ]):
v ( t )=Ri (t)
- For capacitors (unit = farad [F]):
dv
i (t )=C (t)
dt
- For inductors (unit = henry [H]):
di
v ( t )=L (t)
dt
- Kirchhoff’s current law states that the sum of all currents at a node must be
zero.
- Kirchhoff’s voltage law states that the sum of all voltages in a loop must be
zero.
Falling bodies:
Standard first order linear model:
- A standard model for many first order linear initial value problems is:
dx
=kx , x ( t 0 )=x 0
dt
- This is a standard model for:
o Bacterial growth,
o Population growth,
o Radioactive decay,
o Warming and cooling,
o Mixing,
o Simple electric circuits,
o Etc.
Heating and cooling:
- IVP’s dealing with heating and cooling usually follow Newton’s law of cooling:
dT
=−k ( T −T ∞ )
dt
Electrical circuits:
- For resistors (unit = ohm [Ω ]):
v ( t )=Ri (t)
- For capacitors (unit = farad [F]):
dv
i (t )=C (t)
dt
- For inductors (unit = henry [H]):
di
v ( t )=L (t)
dt
- Kirchhoff’s current law states that the sum of all currents at a node must be
zero.
- Kirchhoff’s voltage law states that the sum of all voltages in a loop must be
zero.
Falling bodies:
