The Classical Wave Equation: A Guide to Theoretical Concepts for Enhanced Student Understanding

Aims/Objectives: To develop an intuitive guide for enhanced students' understanding of the classical one-dimensional wave equation, bridging the gap between theoretical derivations and practical applications. The focus was on understanding wave propagation by modeling the elastic properties of a beam structure as a one-dimensional string.
Study Design: The study employed foundational principles and theoretical derivations, and extended into the application of Fourier series techniques to elucidate concepts not typically covered in engineering mathematical textbooks.
Methodology: Analytical and numerical methods were utilised to reinforce critical concepts, making abstract ideas tangible for students. Numerical analysis aids in understanding the theory by demonstrating the evolution of wave patterns, aligning with the analytical solution.
Results: The comparison of analytical and numerical solutions revealed that different time step values (△ t) influence the numerical solution only by shifting the functionin, ƒ(x) in amplitude, but its shape and agreement with the analytical solution was maintained.

Conclusion: This research showcased how innovative teaching techniques, combining analytical and numerical methods, can be used to enhance students' understanding of mathematical theory and its applications in engineering.