Differential Equations

The Differential Equations course introduces students to the fundamental concepts, methods, and applications of ordinary differential equations. The course covers first-order and higher-order differential equations, solution techniques, initial value problems, systems of differential equations, and basic applications in science and engineering. Special attention is given to mathematical modeling, analytical thinking, and the interpretation of solutions in real-world contexts.

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Differential Equation

The Differential Equations course provides students with a systematic understanding of differential equations as an essential tool in modern mathematics, engineering, computer science, physics, economics, and applied research. The course focuses on equations that describe relationships between functions and their derivatives, helping students analyze dynamic processes and changes in real systems. Students study ordinary differential equations of the first and higher orders, methods for finding general and particular solutions, initial and boundary value problems, and systems of differential equations. Special attention is given to analytical methods such as separation of variables, substitution, linear equations, homogeneous and non-homogeneous equations, and equations with constant coefficients. The course also emphasizes mathematical modeling through practical examples, including population growth, motion, heat transfer, electrical circuits, and mechanical vibrations. By the end of the course, students will be able to classify differential equations, choose appropriate solution methods, solve applied problems, and interpret mathematical results in practical contexts.

Team

Mamatova Gulnar Ugizbayevna

Mamatova Gulnar Ugizbayevna is an Associate Professor of the Department of MCM and a Candidate of Technical Sciences. She teaches the courses Differential Equations, Mathematical Analysis, Probability Theory, and Numerical Methods. In her teaching practice, she combines strong fundamental mathematical training with a practice-oriented approach, paying special attention to the development of students’ analytical thinking, modeling skills, and ability to solve applied problems.