AppMaths B242 Better - 9.9

Describe the path independence of a vector field along a curve C:

• What it means for the work done along that curve

• define it

Describe what is meant by a conservative field:

Describe the fundamental theorem with regards to the line integral of a vector field along a curve r(t)

State the condition for the independence of a line integral in an open region R

State the condition of independence of path for a line integral in a closed region

Describe the test for seeing if a vector field is conservative

Solve:

Describe conservative vector fields in 3d-space:

• Write the line integral

• write the condition for path independence

• relate the curl of the vector fields to its conservative nature