Multivariable Calculus takes the concepts learned in the single variable calculus course and extends them to multiple dimensions. Topics discussed include: vector algebra; applications of the dot and cross product; equations of lines, planes, and surfaces in space; converting between rectangular, cylindrical, and spherical coordinates; continuity, differentiation, and integration of vector-valued functions; application of vector-valued functions such as curvature, arc length, speed, velocity, and acceleration; continuity, limits, and derivatives of multivariable functions, tangent planes and normal lines of surfaces; applying double and triple integrals to multivariable functions to find area, volume, surface area, mass, center of mass, and moments of inertia; vector fields; finding curl and divergence of vector fields; line integrals; conservative vector fields, conservation of energy; Green`s Theorem; parametric surfaces, including normal vectors, tangent planes, and areas; orientation of a surface; Divergence Theorem; and Stokes`s Theorem. This course is designed as an additional math course for those students who have successfully completed AP Calculus BC and have an interest in continuing their mathematical studies while in high school. This course counts as state elective credit.
Prerequisite & Recommendations:
Prerequisite: Calculus BC AP
Why Multivariable Calculus?
- Study advanced mathematics beyond AP Calculus BC while in high school
- Advanced Calculus coursework is generally required for science, engineering, and mathematics majors
Who should consider taking Multivariable Calculus?
- Students who have accelerated their math coursework to complete AP Calculus BC by junior year or earlier:
- Want to continue the study of Calculus beyond AP Calculus BC
- Want advanced mathematics coursework to support college/career plans in STEM field