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EauDm Today Calculus refresher

Gradient and directional derivative

Let f Ix y1 be a function ix g E R2

Gradientof otology Iffy

Gives thedirectionof maximum change off at ix yl

Directional derivative let B Iz a vector

Fos f B Tf r f x t ra f yProvides information on how f changes ni the

direction of B

Chain rule for partial derivativesGiven X y consider new coordinates i.e widependent

variables I yn such that

I Thi y changeof coordinates

y yTxiy

EHR How are off fly relatedto iffy

6 Chain rule for several variables

Eet IIFfog off toffs

F tat us

Differentiation and integration areinverseoperations

i ff ki dx f IN t C

ii f fields fix fix I