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**.