COURSE GOALS
MTH 255

• 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.