Mathematics III (PDE, Probability & Statistics)

This course equips engineering students with essential mathematical tools for modeling and analyzing complex physical systems. It is divided into three core modules: Partial Differential Equations (PDEs): Students learn to formulate and solve first and second-order PDEs, classify them, and apply methods such as D’Alembert’s solution, Duhamel’s principle, and separation of variables. Applications include heat conduction, wave propagation, and vibrational problems in mechanical and thermal systems. Probability Theory: This section introduces foundational concepts like random variables, probability distributions, expectation, and moments. It also covers key discrete and continuous distributions relevant to real-world data modeling. Statistics: Focused on data interpretation, students explore sampling, estimation, hypothesis testing, correlation, and regression analysis—crucial for engineering applications involving uncertainty and decision-making under variability. Together, these modules provide the analytical backbone needed for advanced subjects in fluid dynamics, thermodynamics, signal processing, and beyond.