Differential Equations: From Foundations to Modern Applications

By: Zakia Tebba

This work provides a comprehensive study of both the theoretical and practical aspects of ordinary and partial differential equations (ODEs and PDEs). The theoretical framework begins with a detailed classification of differential equations, progressing systematically from first- and second-order ODEs to higher-order equations. It presents key analytical solution methods, including separation of variables, the integrating factor method, and Bernoulli's method, alongside essential solution techniques for PDEs. To bridge theory and computation, the study covers fundamental numerical approaches such as Euler's method, the improved Euler method, and the Runge-Kutta method. On the practical side, the work highlights the efficiency and power of mathematical modeling in analyzing complex dynamical systems; this includes various physical and engineering applications, as well as the implementation of PDEs to model heat diffusion and brain tumor growth. Ultimately, this book aims to deliver a deep yet simplified understanding of differential equations, serving as an invaluable resource for both theoretical analysis and real-world scientific applications.

• Format: Paperback
• Language: English
• ISBN: 3389210806
• ISBN13: 9783389210802
• Release Date: July 2026
• Publisher: Grin Verlag
• Length: 148 Pages
• Weight: 0.41 lbs.
• Dimensions: 8.3" x 0.3" x 5.8"