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19 Cards in this Set

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What are the 2 formulas you need to know for Euler's formula?
Δy = m*Δx
and
y2 = y1 + Δy
When does Euler's method give an overestimate.

When does Euler's method give an underestimate.
When f(x) is concave down.

When f(x) is concave up.
When n increases by a factor of p in Simpson's rule, what does the error decrease by?
It decreases by a factor of p^4.
Give the formulas for Newton's Law of Cooling
dT/dt = -k(T-te)
T = Temperature of object
te = temperature of the room

T = ts - C*e^(-kt)
ts = the starting tempertature of the object.
C = ts - te
Name Kirchhoff's Laws:
IR + L(dI/dt) = E
Ohms Henries Volts
Give Kirchhoff's Law for a capatictor:
R(dQ/dt) + Q/C = E
Ohms 1/farads Volts
Give the Logistic Growth Pattern Formulas
dP/dt = kP(1-P/K)
K = Carrying Capacity
k = rate of change

P = K/(1+Ae^(-kt))
A = K/Po - 1
What equation do you use to figure out what case you're dealing with for Yc?
sqrt(b^2 - 4ac)
> over
= critical
< under
How do you determine ά and β in the underdamped case?
ά = -b/2a
β = sqrt(4ac-b^2)/2a
What is the formula for the underdamped case?
e^(άx)*[C1*cos(βx)+C2*sin(βx)]
When there is no damping or driving force, what is ω?

What is the formula for x(t)

What is this case called?
ω = squt(k/x)

x(t) = C1*sin(ωt) + C2*cos(ωt)

Simple Harmonic Motion
How can x(t) = C1*sin(ωt) + cos*C2(ωt) be rewritten?

What does δ represent?
??????????
x(t) = A(ωt + δ)
A = amplitude = sqrt(C1^2 + C2^2)

δ = the phase angle
What are the 2 formulas for δ in dealing with the simple harmonic motion?
cos(δ) = -C1/A

sin(δ) = -C2/A
What is c?

What is k?
c is the damping constant. Goes with y'.

k is the spring constant. Goes with y.
Write out the master SPRING formula
m(d2x/d2t) + c(dx/dt) + ky = x(t)
List Kirkarroff's differential formula.
L(d2Q/dt2) + R(dQ/dt) + (1/C)Q = E(t)
Henries Ohms Ferads Volts
What is δ?

What is φ?
δ is the phase angle.

φ is the phase shift.
Give the formulas for δ and φ involving sin and cos.
sin(φ) = C1/A
cos(φ) = C2/A
sin(φ) = -C2/A
cos(φ) = -C1/A
Give the formula for frequency.
f = ω/(2π)