13 terms

how do you find new y value using euler's method

y(new)= Y(old)+hy'

what are different about initial value problems

just solve like normal and then use initial values to find the constant

how to find orthogonal trajectories

-solve for k

-differentiate y implicitly in in family one and sub in k value

-solve for y'

-the new dy/dx you are looking for is -1/(y' value just found)

-use separable diff eq techniques to solve and find equation

-differentiate y implicitly in in family one and sub in k value

-solve for y'

-the new dy/dx you are looking for is -1/(y' value just found)

-use separable diff eq techniques to solve and find equation

first order linear diff eq

form: dy/dx + p(x)y = q(x)

y' + (1/x)y = 2

-multiply both sides by I(x) where

i(x) = e^ (int(p(x)dx)

- integrate both sides

-solve for y

function on the left that is prime should be (I(x)y)'

-dont forget + C

y' + (1/x)y = 2

-multiply both sides by I(x) where

i(x) = e^ (int(p(x)dx)

- integrate both sides

-solve for y

function on the left that is prime should be (I(x)y)'

-dont forget + C

how to write domain

D = {(x,y) | x>2, x+y = 1}

three variable:

D= {(x,y,z) (e fork symbol) R^3 | z>y}

three variable:

D= {(x,y,z) (e fork symbol) R^3 | z>y}

little squeeze thrm

make both sides of f(x,y) abs value

separate out part of numerator

set less than or equal to separated out thing

show that the other stuff is less than one

show lim as separated out variable appr 0

separate out part of numerator

set less than or equal to separated out thing

show that the other stuff is less than one

show lim as separated out variable appr 0

when proving a limit dne

try

y=0

x=0

y=x

x=y

y=-x

etc

y=0

x=0

y=x

x=y

y=-x

etc

story problems (mixing)

dy/dx = rate in - rate out

in kg/min (or other v/t)

in kg/min (or other v/t)

equation of a plane

linear: ax+by+cz=d

known-point:z-zo=A(x-xo) + B(y-yo)

known-point:z-zo=A(x-xo) + B(y-yo)

total differential dz

dz= partialz/partialx(dx) + Partialz/partialy(dy)

dz approximates delta z

use delta x and y for dx and dy

dz approximates delta z

use delta x and y for dx and dy

chain rule

dz/dt= parz/parx(dx/dt) + parz/pary(dy/dt)

think tree diagram

think tree diagram

implicit diff

dy/dx = -Fx/Fy

logistic model terms

p-population

m=carrying cap

k-growth rate

A-random variable you find

dp/dt= kp(1-p/m)

p(t) = m/(1+Ae^-kt)

a=m-po/po

m=carrying cap

k-growth rate

A-random variable you find

dp/dt= kp(1-p/m)

p(t) = m/(1+Ae^-kt)

a=m-po/po