Ordinary Differential Equations

The book offers both direct analytic methods for solving Ordinary Differential Equations (ODEs) and approaches for approximate and numerical solutions. This is particularly relevant because many real-world and engineering models rely on ODEs that cannot be solved exactly. Additionally, the book covers mathematical modeling, providing clear instructions on how to create differential equations that represent real-life situations. It also analyzes common mistakes students make while studying ODEs, with exercises designed to help reinforce understanding of these errors. Furthermore, the book includes explicit numerical algorithms and MATLAB codes for solving specific ODEs, particularly in applications within the natural sciences. Many of the numerical methods presented address nonstandard situations where boundary conditions cannot be applied directly to the problem at hand. While the book is accessible to undergraduate students, the inclusion of Chapters 5, 6, and 7 ensures its relevance for graduate students and professionals involved in the mathematical modeling of natural phenomena and their applications in engineering and industry.