Most moving objects don't move in a straight line. Most forces don't act precisely in the direction of motion. Gravity pulls. Water swirls.
Vector Calculus takes the ideas developed in one and two-variable calculus and applies them to the physics of two and three-dimensions. As we explore the development of these ideas, how you think about the world will change. From the complication of the formulas for gravitational attraction emerges the beauty of Kepler's laws. From electromagnetism emerges Maxwell's equations. Vector Calculus is the language of applied calculus.
The true beauty of Vector Calculus, however, lies in its ability to elucidate the connections between geometric objects and their analytic properties. The emphasis of our class will be on these links and the insights they give us into the mathematical and physical world.
