Sequences

Sequence

Students learn/review how to do integrals in a multivariable context, using the vector differential \(d\vec{r}=dx\, \hat{x}+dy\, \hat{y}+dz\, \hat{z}\) and its curvilinear coordinate analogues as a unifying strategy. This strategy is common among physicists, but is NOT typically taught in vector calculus courses and will be new to most students.

Activities

Computational Activity

120 min.

Electrostatic potential and Electric Field of a square of charge

Students write python programs to compute the potential due to a square of surface charge, and then to visualize the result. This activity can be used to introduce students to the process of integrating numerically.

integration electrostatic potential surface charge density
Found in: Computational Physics Lab II course(s) Found in: Computational integrating charge distributions sequence(s)

Small Group Activity

30 min.

Vector Integrals (Contour Map)

Students explore path integrals using a vector field map and thinking about integration as chop-multiply-add.

E&M Path integrals