Advanced Differential Equations

Advanced Differential Equations is a book that covers high-level topics in ordinary differential equations and dynamical systems, utilizing easier notations and multiple examples to deliver difficult material. It covers existence and uniqueness, dynamics of systems, stability, eigenvalues, delay differential equations, fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.

Format: Paperback / softback
Length: 364 pages
Publication date: 22 April 2022
Publisher: Elsevier Science & Technology

Advanced Differential Equations is a comprehensive textbook that delves into the realm of ordinary differential equations and dynamical systems, presenting high-level topics with clarity and accessibility. The book adeptly handles complex concepts, employing user-friendly notations and numerous illustrative examples to facilitate understanding. It organizes its content into distinct sections, each dedicated to exploring key themes such as the existence and uniqueness of solutions for scalar and systems of differential equations, the dynamics of systems, encompassing stability analysis with practical examples and an in-depth examination of the eigenvalues of an associated linear matrix. Furthermore, the book provides comprehensive coverage of existing literature, making it an invaluable resource for scholars seeking to delve into the field.

The text employs a diverse range of approaches, from the eigenvalues perspective to the application of the Lyapunov direct method, enabling students to study stable and unstable manifolds, as well as bifurcations. Additionally, the book extends its scope to include the study of delay differential equations, spanning from ordinary differential equations to the extension of Lyapunov functions to Lyapunov functionals. In the concluding section, the text delves into fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations, offering a comprehensive exploration of these advanced topics.

By presenting the material in a structured and engaging manner, Advanced Differential Equations serves as an essential resource for advanced undergraduate and graduate students in mathematics, physics, engineering, and related fields. Its comprehensive coverage, coupled with its user-friendly approach, equips students with the necessary tools to excel in their studies and pursue careers in the fields of differential equations and dynamical systems.

Weight: 450g
Dimension: 235 x 191 (mm)
ISBN-13: 9780323992800