- Infinite series of nonnegative terms and general series. Absolute and conditional convergence. Power series.
- Vector algebra. Dot product, cross product and box product.
- Analytic geometry of a line and a plane. Parametric equations for a line. Canonic equations for a plane. Points, lines and planes in space.
- Vector-valued functions. Derivative. Parametrized curves. Tangent lines. Velocity and acceleration. Integration of the equation of motion.
- Surfaces in space. Quadric rotation surfaces. Cylindrical and spherical coordinates.
- Scalar functions of several variables. Scalar field. Level surfaces. Limit and continuity. Partial derivatives. Directional derivative. Gradient vector. Differential. Tangent plane and normal line. Chain rules. Implicit function and its derivative. Taylor and MacLaurin formulas. Local extreme values. Absolute maxima and minima on closed bounded regions.
- Vector-valued functions of several variables. Vector field. Field curves. Divergence and curl.
- Line and path integrals. Work, circulation. Conservative fields. Potential function.
- Double integral and its applications. Green’s theorem.
- Parametrized surfaces. Tangent plane and normal line. Surface integrals. Flux. Stokes’s theorem.
- Triple integral and its applications. Divergence theorem.