COURSE GOALS
MTH 254

• For students to develop the ability to compute basic vector quantities, including the dot and cross products, and derivatives of vector functions;
• For students to develop a geometric understanding of vectors (without components), including the dot and cross products, and motion in space;
• For students to develop the ability to visualize curves and surfaces in space;
• For students to develop the ability to relate multiple representations of functions of several variables, such as the relationship between graphs and level sets;
• For students to develop the ability to evaluate partial derivatives, including fluency with the chain rule;
• For students to develop the ability to interpret partial derivatives as rates of change;
• For students to develop the ability to set up optimization problems involving several variables;
• For students to develop the ability to evaluate the gradient of a function;
• For students to develop the ability to interpret the gradient geometrically, including its relationship to level sets;
• For students to develop the ability to evaluate the directional derivative of a function;
• For students to develop the ability to interpret directional derivatives geometrically.
• For students to develop the ability to evaluate multiple integrals;
• For students to develop the ability to set up multiple integrals in standard coordinate systems;
• For students to develop the ability to interpret the domain of multiple integrals geometrically.