Multivariable and Vector Calculus

Course content

Vectors and analytic geometry in 3-space. Functions of several variables: limits, continuity, partial derivatives. Chain rule. Directional derivatives. Tangent planes and linear approximations. Extreme values. Lagrange multipliers. Double integrals, Double integrals in polar coordinates. General change of variables in double integrals. Surface parametrization and surface area in double integrals. Triple integrals in Cartesian, cylindrical and spherical coordinates. Parametrization of space curves. Line integrals. Path independence. Green's theorem in the plane. Surfaces and surface integrals. Flux integrals; gradient, divergence and curl. The divergence theorem in 3-space, Stokes` theorem, Fundamental Theorem of Vector Calculus.