For students to develop a geometric understanding of vectors (without components), including the dot and cross products.
For students to develop the ability to express vectors in standard coordinate systems and bases.
For students to develop a geometric understanding of the gradient, including its relationship to level sets.
For students to develop a geometric understanding of conservative vector fields, including their relationship to the gradient and to level sets.
For students to develop the ability to evaluate line and surface integrals;
For students to develop a geometric understanding of the curl and divergence, including their relationship to circulation and flux.
For students to develop the ability to evaluate the curl and divergence of a vector field in standard coordinate systems.
For students to develop a geometric understanding of the Divergence Theorem and Stokes' Theorem.
For students to appreciate the unifying thread brought to these topics by the use of a “use what you know” strategy starting from the vector differential.