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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)