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This course provides a comprehensive introduction to mathematical modeling techniques, equipping students with essential skills to analyze and solve complex real-world problems using mathematical tools. It begins with foundational concepts, including power series, differential equations, and Laplace transforms, and gradually explores specialized topics such as Bessel functions, Legendre polynomials, and simulation models.The course delves into both theoretical and applied aspects, covering methods for solving differential equations, generating random numbers, and modeling deterministic and probabilistic systems. Additionally, students will engage in optimization modeling, learning linear programming methods including geometric and algebraic solutions, as well as the Simplex Method and sensitivity analysis. By the end of the course, students will be adept at applying mathematical modeling to a variety of disciplines, making it a valuable resource for further study or practical application in engineering, physics, economics, and beyond.
