MATE-1208 Vector Calculus (Honors)

Curves on a plane and in space. Cylindrical and quadric surfaces. Straight lines and planes. Partial derivatives, chain rule. Differentiation in scalar and vector fields: definitions, techniques and applications. Notion of gradient. Maximums and minimums of functions with more than one variable. Lagrange multipliers. Line, multiple, surface and volume integrals. Theorems of Green, Stokes and Gauss. Physical and geometric applications. The difference between this course and MATE-1207 is not the content, but rather the depth of the topics discussed.