Topic Area 1: Differential Calculus and Its Applications

1. Investigation of extrema (local, constrained, global) of real functions of several variables using partial derivatives.

2. Partial derivative, definition of directional derivative, gradient (definition and geometric interpretation), differentiability.

3. Limit, continuity, and differentiability of a real function of a real variable at a point and on a set.

4. Application of differential calculus in analyzing the behavior of a function (extrema, monotonicity, convexity, asymptotes of the function graph).

Topic Area 2: Integral Calculus and Its Applications

5. One-dimensional and two-dimensional Riemann integral, its construction, properties, and methods of computation.