A.B Urdaletova, PhD – Professor, Mathematics, Kyrgyz-Turkish MANAS University, Bishkek, Kyrgyz Republic
S.K. Kydyraliev, PhD – Professor, Mathematics, American University in Central Asia, Bishkek, Kyrgyz Republic

Series: Mathematics Research Developments
BISAC: MAT007010; MAT030000; MAT027000
DOI: https://doi.org/10.52305/PKFN3674

Book Review
“The Direct Integration of Ordinary Differential Equations deserves high praise. It combines mathematical rigor, practical focus, and a wide range of applications. The book will be useful both in academic teaching and for researchers seeking efficient methods for solving applied problems.” To read the full review, click here.>>> – Professor Asan Baizakov, PhD, Head of the Laboratory of the Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic

Book Description
The process of solving an ordinary differential equation can be reduced to one or, in the case of high-order equations or systems of such equations, to several integration operations. This work is devoted to the presentation of such methods — the methods of direct integration, developed by the authors.

A Nobel laureate, the outstanding physicist L. D. Landau (1908-1968) once wrote, “For the study of theoretical physics, first of all, knowledge of mathematics is necessary. What is needed is not all kinds of theorems about existence, which mathematicians are so generous with, but mathematical technique, that is, the ability to solve specific mathematical problems. First, you need to learn how to correctly differentiate (and, if possible, quickly), integrate and solve ordinary differential equations in quadrature; as well as the study of vector analysis and tensor algebra (that is, the ability to operate with tensor indices). The main role in this study should be played not by the textbook, but by the problem book – which one is not very important, the main thing is that it has enough tasks. I am categorically convinced that all theorems about existence, excessively strict proofs, etc., should be completely banished from mathematics studied by physicists”. Agreeing with these words said to specialists in theoretical physics, we believe they are equally true for specialists in all fields of engineering, economics and other sciences. Therefore, special attention should be paid to methods that allow the direct integration of ordinary differential equations. Unfortunately, there are hardly any books in which differential equations can be studied in the way that Landau suggested. We believe this work will fill this gap.