Chapter 7 does not aim to be a comprehensive treatment of the discipline of differential and integral calculus, but rather to clarify the fundamental concepts and develop the main techniques. After introducing the usual topology of real vector spaces, it presents their nonstandard extension and proves basic theorems about continuous functions. It then establishes the rules of differential calculus, defines the integral as a sum of infinitesimal rectangles, and develops some key integrals such as those of the exponential, logarithmic, and basic trigonometric functions. The final part is devoted to intuitively clarifying the meaning of partial derivatives, differentiation in several variables, and the concept of the total differential, which acquires an intuitive meaning when viewed from the nonstandard perspective.