Course Description
Honors multivariable calculus is equivalent to Calculus III in college for scientists and engineers. Students continue their studies from AP Calculus BC by applying calculus in a more general lifelike context, analyzing functions that deal with multiple dimensions. Students explore vector-valued functions, which describe motion in two and three dimensions and learn vector algebra, making connections with science and economics concepts. Next, students generalize one-dimensional calculus to the differential and integral calculus of functions of several variables. They consider partial derivatives, extrema in several variables, Lagrange multipliers, multiple integrals, and line and surface integrals. Students then turn their attention to Vector Calculus, where students connect the concepts of vector functions and functions of several variables in multiple dimensions through Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem. Finally, the course ends with the study of second-order differential equations. Students will use a computer algebra system to simplify complex mathematical expressions and 3D graphing software to visualize and manipulate three-dimensional objects. A graphing calculator is required for this course. Upon completion of this course, students will be well equipped to place out of Calculus III at the college level. Prerequisites: completion of AP Calculus BC and departmental approvalÂ
Textbook and Reference Materials
Sections Taught