The course Mathematical Analysis is designed to provide students with a strong foundation in the fundamental concepts and methods of higher mathematics. The discipline introduces key topics such as functions, limits, continuity, derivatives, integrals, sequences, series, and functions of several variables. These concepts form the theoretical basis for many areas of science, engineering, computer science, economics, and applied research. During the course, students learn how to analyze the behavior of functions, determine limits, investigate continuity, calculate derivatives, and apply differentiation techniques to solve practical problems. Special attention is given to the use of derivatives in studying monotonicity, extrema, optimization problems, and graph construction. The course also covers integral calculus, including indefinite and definite integrals, methods of integration, and applications of integrals to the calculation of areas, volumes, and other real-world quantities. In addition, students develop logical thinking, analytical reasoning, and mathematical problem-solving skills. They learn to interpret mathematical formulas, understand graphical representations, and connect theoretical concepts with practical applications. Mathematical Analysis helps students build the necessary mathematical background for further study of differential equations, probability theory, numerical methods, mathematical modeling, and specialized professional disciplines. By the end of the course, students are expected to understand the main principles of mathematical analysis, apply analytical methods correctly, solve standard and applied problems, and use mathematical language accurately in academic and professional contexts.