MATH 3001 Study Guide - Final Guide: Linear Map
APPM 2360 Exam 1, Review 1
IVPs: Consider the differential equation dy
dt =t
t2y+y.
(1) Find the general solution for this DE.
(2) Find the solution for this DE that passes though the point (1,2).
Picard’s Theorem: T/F + Explanation: Both conditions of Picard’s Theorem hold for the following IVP:
dv
dt =kv2/3,
v(3) = 4.
Linear Operators: Show that L(y) := y′+ty2fails to be a linear operator.
Mixing: A tank initially contains 2000 gallons of water containing 400 pounds of salt. Fresh water is pumped
into the tank at the rate of 50 gallons per minute and a well-mixed solution is being drained from the tank
at the rate of 100 gallons per minute. Determine the number of pounds of salt remaining in the tank when
the tank holds 1000 gallons.
Stability & Equilibria: Consider the Predator-Prey model given by
dR
dt = 2R(1 −R)−RB,
dB
dt =−B+RB
2.
Determine and plot the nullclines and equilibrium points for the system.
Document Summary
Ivps: consider the di erential equation dy dt t t2y + y (1) find the general solution for this de. (2) find the solution for this de that passes though the point (1, 2). Picard"s theorem: t/f + explanation: both conditions of picard"s theorem hold for the following ivp: dv dt. Linear operators: show that l(y) := y + ty2 fails to be a linear operator. Mixing: a tank initially contains 2000 gallons of water containing 400 pounds of salt. Fresh water is pumped into the tank at the rate of 50 gallons per minute and a well-mixed solution is being drained from the tank at the rate of 100 gallons per minute. Determine the number of pounds of salt remaining in the tank when the tank holds 1000 gallons. Stability & equilibria: consider the predator-prey model given by dr dt db dt.
