Painting by numbers
Today, I am very much painting by numbers – completing the final assignment question through mechanical computation devoid of intuition or understanding.
Linking line integrals, curl, grad and potential functions into something meaningful has eluded me. It seems, and remains, a messy mystery, not helped by my lack of understanding of exactly what “work done” really means, what decides if a line is path dependent or path independent, and what it means to classify vector fields as conservative or non-conservative.
Follow the structures outlined in the unit, get an answer, check answer agrees with that in the unit, peer at some output, wonder what it means in the real world, re-read chapter, arrive at same point, repeat to fade….
I am avoiding any part three vector calculus questions in the exam, that much is for sure.
I expect the result on TMA6 will be ok but will over-reward my utter, utter lack of understanding. While the separate entities of div, curl and grad are easy enough to get an intuitive feel for, the whole vector calculus picture is as muddied as a hippo’s home.
Personal difficulty with this unit, out of ten: 10.