Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Calc 2 Final
| Question | Answer |
|---|---|
| What is a differential equation? | An equation involving an unknown function y(t) and its derivatives. It is relating a function and its derivative. |
| What is the difference between autonomous and pure time differential equations? | Pure time only involves time as a variable of the equation (example: dy/dt=g(t)). Autonomous involves y as a variable (example: dy/dt=g(y)) |
| What is meant by the 'order' of a differential equation? | It's how many derivatives we're taking |
| How does one tell if an autonomous DE is locally stable or unstable? | If the derivative is negative, it is locally stable. If it is positive, it is unstable. |
| What is the formula for Euler's Method? | y (sub n+1) = y (sub n) + h * [F(t (sub n), y (sub n))] where h= step size and F(t, y) = t+y |
| What is the Lotka-Volterra Equation that models a predator population, M (with the prey population represented by D)? | dM/dt= (-k*M)+(b*D*M), where (-k*M) represents the predator population decreasing if they don't feed, and (b*D*M) representing how feeding on prey increases the birth of new predators. |
| What is the Lotka-Volterra Equation that models a prey population, D (with the predator population represented by M?) | dD/dt= (r*D)-(a*D*M), where r is the rate of prey birth, and a is the rate at which they are eaten |
| What is the chain rule? | d/dx [f(g(x))] = f'(g(x)) * g'(x). AKA, f*g = f' * g + g' * f |
| What is a separable differential equation? | It is a DE of the form dy/dt= f(t) * g(y) |
| What are the steps for evaluating a separable differential equation, dy/dt= (some mess)? | 1.) multiply by dt and move t's to one side. 2.) Integrate both sides (remember c!) 3.) Solve for y. Now we have y= (an equation). Yay |
| How do we solve a separable equation with an initial condition (example: y(0)=5) | Once a separable equation has been turned from dy/dt=(mess) into y=(equation+c), if y(0)=5, then we plug in 5 for y and 0 for all of the t's in the equation, and solve for c. |
| What is the derivative of tan(x)? | sec^2(x) |
| What is the derivative of sec(x)? | sec(x)tan(x) |
| What is the derivative of cot(x)? | -csc^2(x) |
| What is the derivative of csc(x)? | csc(x)cot(x) |
Created by:
clownestate