Integration

Question 1

Trap Rule - how to use the sigma section

Answer 1

Top of Sigma is n-1 (n being number of traps).

then x_i = i * width of trap

Question 2

Partial Derivative Notation

Answer 2

Right to left when doing it with the funny b notation

otherwise it’s as expected

just manually expand it

Question 3

Stationary Points Multivariable

Answer 3

D = fxx*fyy-(fxy)^2

if D>0 and fxx>0, local minima
if D>0 and fxx<0, local maxima

Saddle point when D<0

Inconclusive when D=0