Unit Gradient fn -...

25
Unit Gradient fn i i f

Transcript of Unit Gradient fn -...

Page 1: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

Unit Gradient

fn

i i

f

Page 2: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

Plooflet Fct bea parametrizahoof f c

What is

dat fCrTIt is 0We do not change

Page 3: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

geheight when

mooing along f c

Now use thechain rule

Tf crit D I CH so

t

LAG

Page 4: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

farcy 7 thy2

ty2

1

came

rTtkEaI

I 3

Page 5: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

1h 3D

farcy i 21 9

is a surface

f It yEy

Page 6: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

THEE

I

F tamp6fGy 2 fast bytetf

E

9IN

Page 7: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

to

a tbytczd2

tpgna

Page 8: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

D

x72y2tEE4

Find the

tangent planeat A Chill

Or

Page 9: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

If EEE

Tfa HI

Page 10: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

Lz

Thang2x thy 22

d

plug in Atl

8

Page 11: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

D onD

dentate

Dff tf.v

directionalderivative

for the

Page 12: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

for thedirection I

unit vectorIntakes

Slope in thedirection 8

Ft ample

Page 13: Unit Gradient fn - people.math.harvard.edupeople.math.harvard.edu/~knill/teaching/summer2020/handouts/unit… · she is. Steepness And if we go in the dire chore of the gradient the

Empief 4500 x y2F LIE

forgo 10,20

Buf Cairo

Ei D Eid

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2.20 Lys

2

main

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we are goingdown the

a.fncrenkedh.DEflag

Tf I'd

fx

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fxslope when

omoving in the1 directionEast

DepIf GigAid

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as E

In whichdirection do

we have to

move to

increase f

most

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used in

machine leaning

down

iiiX

Laridae

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DEF

f

directional

famethe gradient

Ff VIFfl

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f

I v s Iinnuitor

FEE

Ffl is themaximalshe is

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Steepness

And if we

go in the

dire chore ofthe gradientthe slope is

Ffl

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I sIDuft

Ff Tfffllulosd

a Tfl cost

I Tff

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1

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ofun.tlVfLnff e3

Ffl is themaximal

me

T.fpointscepwadsa.ws

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k 0

then we

are on the

topnett

weekExtrema


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