2 semesters, 1 creditPrerequisite: AP Calculus BC with a minimum grade of B, and department recommendation
This advanced course begins with an investigation of vectors in XYZ space, their dot and cross products, and the use of vectors in determining equations for lines and planes in space. Students then study vector-valued functions, their derivatives, velocity and acceleration vectors, tangent and normal vectors, and the use of vector valued functions in calculating arc length and curvature. Students explore multivariable functions, including limits and continuity, partial derivatives, differentiability, total differentials, the generalized chain rule, directional derivatives, tangent and normal lines, tangent planes, extrema, and optimization. Students then turn their attention to multivariable integral calculus with a study of iterated integrals, double integrals and volume, double integrals with polar coordinates, centers of mass, and surface area. They investigate triple integrals and the volume bounded by surface curves. They study cylindrical and spherical coordinates and delve into how cylindrical and/or spherical coordinates make the computation of some triple integrals much more manageable. Lastly, students turn their attention to vector analysis, line integrals, vector fields, flow and flux, Green's Theorem, the Divergence Theorem, parameterized surfaces, and Stokes' Theorem.