Equations

Question 1

Survival and renewal

Answer 1

P(T) = S(T)P(0) + a/b S(T-t)R(t)dt

a/b: integral from a to b
P(T): population at time T
S(T): survival
S(T-t): survival from time T minus t
R(t): rate of change

Question 2

Cardiac output

Answer 2

A/(a/b c(t)dt
A: total amount of dye
(a/b c(t)dt: concentration of dye
a/b: integral from a to b
c(t): concentration at time t
dt: change in t

Question 3

FTC 1

Answer 3

For the general form of:
d/dt f(x)/g(x) h(t)dt
You get h(g(x))g’(x) - h(f(x))f’(x)

Question 4

FTC 2

Answer 4

For
——a
f(x)|
——b
you get f(a)-f(b)

Question 5

Stability criteria

Answer 5

If g’(y) < 0 then y is a stable equilibrium
If g’(y) > 0 then y is an unstable equilibrium

Question 6

Order for integration by parts for u (not u substitution)

Answer 6

LIATE
L - logarithm
I - inverse trigonometric fxns
A - algebraic fxns
T - trigonometric fxns
E - exponential fxns