Birkhäuser, 2025. — 323 p. — ISBN-13 : 978-3031865312 This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters...
Cambridge University Press, 2025. — 381 p. — ISBN-13 : 978-1009610025 This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems,...
Springer, 2024. — 84 p. — ISBN-13 : 978-9819978786 This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since...
Springer, 2025. — 318 p. — ISBN-13 : 978-3031891410 Inverse problems lie at the core of scientific discovery, enabling us to determine causes from observed consequences. They are fundamental to both theoretical research and technological innovation, making them a central topic in the mathematical sciences. This book explores a cutting-edge area of inverse problems—those related...
De Gruyter, 2025. — 376 p. — ISBN-13 978-3111635514 This book is devoted to the qualitative theory of partial dynamic equations on arbitrary time scales. The results in the book generalize the classical results, and they unify the discrete and continuous cases. The book starts with classification and canonical forms for second-order PDEs. Next, the Laplace transform method and...
Springer, 2024. — 144 p. — ISBN-13 : 978-9819735761 This monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential operators. It focuses on deriving explicit lower and upper bounds for eigenvalues, as well as explicit estimations for eigenfunction approximations. Such explicit error estimations rely...