In a consistent, coherent, and comprehensive presentation, this work emphasizes many analogies: how similar methods can be applied to analogous problems in different areas with their specific interpretations. It gives an overview of the mathematical modeling of physical phenomena and engineering processes, which is unified and includes interdisciplinary areas. The author covers interdisciplinary topics, combing several areas of physics, mixed technologies, and engineering. He explores the interplay between physical laws and mathematical methods as a basis for modeling natural phenomena and engineering devices.