This course is a Multivariable Calculus that extends the theory of integral and differential calculus to functions of many variables. It takes calculus 1 and 2 from the 2-dimensional world of single-variable functions to solid analytic geometry, multi-variable functions, and vector fields.
Some of the topics covered include vector and analytic geometry, directional and partial derivatives, multiple integrals, limits, continuity, and differentiation, Lagrange multipliers, polar and spherical coordinates, inverse matrices, eigenvalues and eigenvectors, matrix algebra, calculus of scalar-valued functions of several variables, Green’s Theorem, triple integrals in rectangular, line and surface integrals, the fundamental theorem for line integrals, Stokes’s theorem, and the Divergence Theorem.
Once the course is successfully completed, students should be able to:
• Differentiate vector and scalar functions
• Solve multiple integrals
• Calculate extreme values using Lagrange multipliers
• Handle vectors easily in solving problems involving the geometry of planes, curves, lines, and surfaces in space.
• Translate real-life situations into the symbolism of mathematics and find solutions for the resulting models.
Pre-requisites: Calculus 1 and Calculus 2