HOSILANING MUHANDISLIK MASALALARIGA TADBIQI

Аннотация

This paper explores the application of derivatives to engineering problems as a practical aspect of mathematical analysis. The derivative is a vital tool to describe rate of change in physical processes, mechanics, electronics, heat transfer, and many other fields. In engineering, it plays a crucial role in solving problems related to structural stability, optimal design, and energy efficiency. Specifically, real- world cases such as identifying extrema points, calculating velocity and acceleration, and modeling thermal variations are effectively addressed using derivatives. The findings demonstrate that mathematical modeling simplifies complex engineering challenges. The study integrates theoretical concepts with numerical methods, and differential equations. Kalit so‘zlar: hosila, tezlik, tezlanish, kuchlanish, monotonlik, ekstremum, optimallashtirish, matematik modellashtirish, differensial tenglama. Ключевые слова: производная, скорость, ускорение, напряжение, монотонность, экстремум, оптимизация, математическое моделирование, дифференциальное уравнение. Keywords: derivative, velocity, acceleration, stress, monotonicity, extremum, optimization, mathematical modeling, differential equation.