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19 Cards in this Set
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 Back
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(Tte)
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(1P/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(4acb^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)
