Differential Calculus

The course covers differential calculus and its applications starting from the basics. We also define and study elementary functions: polynomials, rational functions, trigonometric functions and their inverses as well as exponential and logarithmic functions. The concept of limit is approached computationally rather than rigorously but is illustrated in various ways. The derivative and its applications can be examined more precisely using limits. A key focus is the use of derivatives in analyzing the behavior of functions. Applications of derivatives covered in the course include optimization problems, L'Hôpital's rule, and approximation of functions using Taylor polynomials.