The course provides an essential and solid background for understanding fundamental processes and phenomena in biology, chemistry, physics, and engineering. It extends the main topics of differential and integral calculus for real-valued functions of one real variable to the case of vector-valued functions of one real variable; real-valued functions of several variables; and vector fields. Specific topics include vectors in the plane and space; parametrized curves and surfaces; partial derivatives and gradients; constrained and unconstrained optimization; integration over regions in the plane and space; integration over curves and surfaces; Green’s Theorem, Stokes Theorem, and Divergence Theorem.

Skill Level: Beginner