The book "Methods of separation of variables and quadratic errors and their application to the boundary problems of mathematical physics" by I. Tsai is a deep and comprehensive study that will become an indispensable tool for students, graduate students and professionals in the field of mathematical physics and applied mathematics. This work not only illuminates theoretical aspects, but also offers practical solutions, which makes it especially valuable for those who seek to apply the knowledge gained in real-world tasks. The book focuses on the methods of separating variables one of the most powerful tools in solving differential equations, which are often found in physics. Tsai examines in detail how these methods can be used to solve boundary problems, which is a relevant and sought-after area in modern mathematics. The reader will be able to find here not only theoretical justifications, but also practical examples that will help to better understand how to apply these methods in various situations. The book will be of interest to both students studying mathematical physics and more experienced researchers who want to deepen their knowledge in this area. If you are passionate about mathematics, physics or engineering, then this work will become a real storehouse of knowledge for you. It is also suitable for those who are interested in applied mathematics and are looking for new approaches to solving complex problems. The topics raised in the book cover a wide range of issues related to edge problems, including their mathematical modeling and numerical methods. Tsai not only explains the basic principles, but also immerses the reader in the world of complex mathematical concepts, such as quadratic errors, which play an important role in the analysis and optimization of solutions. This makes the book relevant for those who want not only to learn the theory, but also to learn how to apply it in practice. Style and . Tsai is distinguished by clarity and logical presentation, which allows the reader to easily assimilate even the most complex concepts. The author uses many examples and illustrations, which makes the material more accessible and understandable. This is especially important for those who may encounter difficulties in understanding the theoretical aspects. The book is written with care for the reader, which makes it not only a textbook, but also an interesting reader. In addition, and . Tsai is known for his other work in mathematical physics and applied mathematics, which are also noteworthy. His research and publications have helped many students and professionals to understand complex issues and find effective solutions. If you are interested in works such as "