Fundamentals & Definitions
What is meant by the order of a differential equation?
Highest order derivative present in the equation
What does this diff eq model dP/dt = kP?
Population growth
A man whose mass is 80kg is hanging stationary on a rope: find the tension in the rope.
784 N
What is the first Kolmogorov axiom?
P(A) >= 0 for any event A
Who won the 2026 FIFA World Cup?
Spain
What does it mean that a diff eq is linear?
The dependent variable we are taking the derivative of (typically y) is linear
What does this diff eq model dN/dt = -kN ?
Radioactive decay
Find the solution to the diff eq dy/dx = yx.
y = Ce^(x^2/2)
What is the 2nd Kolmogorov Axiom?
P(S) = 1 where S is the sample space
Which team did Lebron James just sign for?
Philadelphia 76ers
Distinguish between general solution and particular solution.
General solutions contain arbitrary constants while particular solutions are obtained using initial conditions.
Which law is this: Sum of Forces = ma?
Newtons 2nd law of motion
Find the solution to dy/dx = x - 3y
y = x/3 - 1/9 + Ce^(-3x)
What is the 3rd Kolmogorov Axiom?
P(the union of disjoint events A_1, A_2, A_3,...) = P(A_1) + P(A_2) + P(A_3)+....
Which American hedge fund with Noble Prize winners on its board of directors filed for bankruptcy in 1998?
Long term Capital Management
What does Newton's 3rd law state?
For every action there is an equal and opposite reaction.
What is the solution to Newtons law of cooling?
T = T_s + (T_0 - T_s)
You roll two fair die, what is the probability of landing a sum of 7?
1/6
What does DeMorgans Law state?
(A U B)^C = (A^C intersect B^C) &
(A intersect B)^C = (A^C U B^C)
Famous magic gravity ball from the early 2010s.
Fushigi Ball
What is Jerk?
The derivative of acceleration.
What is the solution to the RC Circuit diff eq when solving for charge q(t)?
q(t) = V_B*C(1-e^(-t/RC))
An elevator has a mass of 800 kg. The elevator is initially going down at 10m/s; it slows to a stop with constant acceleration in distance of 25m. What is the tension T in the cable while the elevator is being brought to rest?
9440N
Are the real numbers countably or uncountably infinite?
uncountably infinite
What is the S&P 500's average annual return since its launch in 1957?
~10%