Math cheat sheet - Summary Engineering Calculus PDF

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Math finals cheat sheet...

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Ch1- Partial Derivatives

Ch2- Multiple Integrals

Basic Vector Equations

Double Integrals for Rectangular Domains

Normal Vector :

( )

f x (a , b) n= f y (a , b) −1

∬ c dA = c × area of D , where c is a constant D

Double Integrals for Non-Rectangular Domains *DRAW THE GRAPH OUT* Type 1

⋅ Tangent Vector = 0 v ⋅w=|v||w|cosθ

Normal Vector

Equation

of

tangent

( ) ( ) ( )( ) f ( a,b )

❑

b h (x)

D

a g (x)

)( ) ( )

,

min

f x ( a , b )=0, f y ( a ,b )=0 2 D=f xx f yy − f xy D f xx (a ,b Resul

Lagrange Multipliers Finding the max/min

Line Integrals

f (x,y,z)

g ( x , y , z )= 0 Must satisfy :

g ( x , y , z )= 0

2

❑

d h ( y)

D

c g ( y)

f x =λ g x , f y =λ g y , f z =λ g z

domain

f (x , y , z ) x1 r ( t ) = y1 z1

defined

Double Integrals in Polar Coordinates

along

a

smooth

curve

()

f (¿ x (t ) , y ( t ), z (t)) √(x ( t ) ) +( y ( t ) ) +(z ( t ) ) dt '

2

'

2

'

2

b

∫¿

∬ f ( x , y ) dA=∫ ∫ f ( x , y ) dxdy

a

Finding Min/Max Speed 2

Find |v (t)| ,

t min Max Saddl e

of

a

{ ( x , y ) :c ≤ x ≤d , g ( y )≤ x ≤ h( y ) }

Local Extrema Critical point:

>0...