1. Vectors and analytic space geometry. 2. Norms, convergence of vector sequences, open and closed sets, compact sets. 3. Curves, Frenet frames, surfaces. 4. Functions of several variables. 5. Partial derivatives and their applications, linear approximation, differential, Taylor's formula. 6. Method of Lagrange multiplier. 7. Inverse function theorem, implicit function theorem. 8. Multiple integrals. 9. Green's Theorem. 10. Line and surface integrals. 11. Gauss and Stokes' Theorems.

CILO-1: Recognize partial derivatives, particularly in the area of geometric interpretations and applications in optimization problems. CILO-2: Calculate the multiple integrals, such as double, triple and line integrals. CILO-3: Explain and solve problems related to conservative field and potential functions.