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. 

• Comprehensive direct analytic methods and approximate/ numerical solutions.
• Analyzes common mistakes students make while studying ODEs, with exercises designed to help reinforce understanding of these errors.
• Many examples with nonlinear modeling.

Dr. Ranis Ibragimov is an Associate Professor at Hampton University, VA, and he is an applied mathematician who earned his Ph.D. in Applied and Computational Mathematics from the University of Waterloo in Ontario, Canada. He has extensive research experience in mathematical modeling, differential equations, and geophysical fluid dynamics. His research has been supported by Monbusho Research Fellowship in Japan, NSERC (Natural Sciences and Engineering Research Council of Canada), Fisheries and Oceans Canada  (Federal grant leading for managing Canada's fisheries, its oceans and freshwater resources, and safeguarding its waters) and NSF research grant in the USA. 
His previous teaching and research appointments include: 
Lead Applied Mathematician, GE Global Research, Niskayuna, NY, USA
Associate Professor , University of Texas at Brownsville, USA
Professor, Wenatchee Valley College, USA
Visiting Researcher, NSF Visiting Faculty Research Grant, Pacific Northwest National Laboratory, Department of Energy, USA
His research interests broadly lie in applications of Mathematical Modeling (including Differential Equations, Analytic and Numerical Methods, Perturbation theory, Bifurcation phenomena, Asymptotic Methods, Data Analysis and Statistics) to industrial, engineering, and environmental sciences. As a fluid dynamicist, he is working on geophysical and environmental flows within a complex geometry. While working at GE, he was also participating as a consultant to the U.S. Aerospace industry and research agencies, providing expert advice and guidance on the use of Mathematical Modeling to design and analyze major components and subsystems of aircraft, launch vehicles, and missiles.