dv/dt = .... slope fields how do you determine the order of a differential equation? initial value problem "Find" a differential equation? What should your answer look like?

"Find" a differential equation? What should your answer look like?

v(t) = ... how to tell if a function is a solution to a differential equation? linear first order ODE "Solve" a differential equation? What should your answer look like? "Find" a differential equation? What should your answer look like?

"Solve" a differential equation? What should your answer look like?

when equation includes only 1- independent variable (t) 2- dependent variable of interest (v) 3- model parameter (R) - constants differential equation how to know when you're done solving a differential equation? equilibrium value of slope field how to tell if a function is a solution to a differential equation?

how to know when you're done solving a differential equation?

when all lines, regardless of initial condition, reach the same value differential equation equilibrium value of slope field how to tell if a function is a solution to a differential equation? how to tell if a differential equation is separable?

equilibrium value of slope field

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Calculus - Geometry

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Cards in this deck(14)

an equation relating a quantity and its derivatives

dv/dt = ....

v(t) = ...

when equation includes only 1- independent variable (t) 2- dependent variable of interest (v) 3- model parameter (R) - constants

given dy/dx draw slopes using points and shows shape of curve at points

when all lines, regardless of initial condition, reach the same value

A differential equation with an initial condition

compare the left hand side and the right hand side -take the derivative of the answer equation -plug the answer equation into the original differential equation

ordinary differential equation -has one independent variable

partial differential equation

its the highest order of all (inluding partial) derivatives of dependent variables with respect to independent variables

F is linear if F can be expressed in the following -dont have multiplication of y derivatives -dont have multiplication of y with itself when the product is more than to the power of 2 -dont have transformation on y or derivatives (siny, cosy, e^y)

can be written in the form: M(x) + H(y)y' = 0 everything to do with independent variable and dependent variable is separate

y' + p(t)y = g(t)

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