Week 5 Lagrange Multipliers

Question 1

what are lagrange multipliers used for

Answer 1

find local minima and maxima of a function subject to a constraint

Question 2

what are the requirements for lagrange multipliers

Answer 2

df = dg = 0

del of both f and g must be perpendicular to dS and are parallel or anit-parallel to each other

Question 3

what is the general lagrange multiplier equation

Answer 3

∇f = λ∇g

Question 4

what are the two ways the del operator can act on a vector field

Answer 4

divergence - dot product

curl - cross product

Question 5

what does the divergence operation produce

Answer 5

scalar field

Question 6

what does the curl operation produce

Answer 6

vector field

Question 7

what are the 4 main applications of the div and curl operators

Answer 7

> Simplify the calculation of line and surface integrals
Quantifying the circulation and flux
Determining if a force is conservative
Simplifying and Unifying the laws of electromagnetism