Mathematical models in natural science and engineering

This book originated from the author's lectures on mathematical modeling delivered to students specializing in applied mathematics and computer science at Nizhny Novgorod State University. The lectures have been adapted into a cohesive presentation on mathematical models and modeling. The course emerged due to the contemporary Russian educational system's focus on a blend of fundamental and applied mathematics, which often led students to solve only well-defined mathematical problems. This approach created a disconnect from crucial aspects of real-world problem-solving, such as deeply understanding a specific problem and its mathematical formulation, which includes simplifications, idealizations, and the development and adjustment of mathematical models to align with real systems. Another key aim is to guide university graduates in their future research, encouraging them to engage with mathematics not just as a set of abstract issues, but as a universal language applicable in various fields of exact science. The book emphasizes mathematical modeling as a vital tool for exploring nature, engineering, and human society, fostering a comprehensive understanding of its significance in real-world applications.