The advent of mathematical modeling has significantly impacted various aspects of people's lives and has contributed to advancements in civilization and the exploration of new frontiers. Scientific modeling is a fundamental component of modern research, offering a method for both qualitative and quantitative representation of processes, phenomena, or objects through numerical models. These models are developed using mathematical tools that effectively capture the essence of the real-world processes, phenomena, or objects being studied.

A thorough examination of the history and application scope of mathematical modeling reveals its profound influence in simplifying human life and addressing pressing challenges faced by humanity. This includes an exploration of both the benefits and limitations associated with scientific modeling. Additionally, this study delves into the utilization of computer programs, particularly Python, for simulating physical phenomena.

This work encompasses various aspects of scientific modeling, ranging from its historical origins to the classification of numerical modeling techniques and models. Practical experiments on modeling free harmonic motions, such as second-order thermal conductivity, using Python's scientific packages with the capability to manipulate input data are also presented. Through these endeavors, valuable insights into the intricacies of mathematical modeling and its practical applications are gained.