Master the calculus of functions of two and three variables. Starting with vectors and vector-valued functions, you will learn partial derivatives, gradients, multiple integration, and the powerful theorems of vector calculus — Green's, Stokes', and the Divergence Theorem. This course builds the mathematical foundation essential for physics, engineering, and advanced mathematics.
Build fluency with vectors in two and three dimensions and study curves defined by vector-valued functions
Extend differentiation to functions of several variables using partial derivatives, gradients, and directional derivatives
Evaluate double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates
Study vector fields and learn to compute line integrals of scalar and vector fields along curves
Parametrize surfaces and compute surface integrals of scalar functions and vector fields
Master the three great theorems of vector calculus that generalize the Fundamental Theorem of Calculus to higher dimensions
A 20-question comprehensive assessment covering all modules in this track.