Multiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume begins with a basic introduction to multiplicative differential equations and then moves on to first and second order equations, as well as the question of existence and unique of solutions. Each chapter ends with a section of practical problems. The book is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Multiplicative Differential Equations: Volume 2 is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second order multiplicative linear and nonlinear equations are explored. The authors also present first order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The book is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Volume 1: 1.Introduction. 2. Elementary First Order MDEs. 3. First Order Multiplicative Linear Differential Equations. 4. Second Order Linear MDEs. 5. Existence and Uniqueness of Solutions.
Volume 2: 1. Systems Multiplicative Differential Equations. 2. Qualitative Analysis of Multiplicative Differential Systems. 3. Stability Theory. 4. Multiplicative Linear Boundary Value Problems. 5. Multiplicative Nonlinear MDEs. 6. First Order MPDE.
Biography
Svetlin G. Georgiev is a mathematician who has worked in various areas of study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He is also the author of Dynamic Geometry of Time Scales, CRC Press//Taylor & Francis Group. He is a co-author of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson, CRC Press/Taylor & Francis Group. Khaled Zennir earned his PhD in mathematics from Sidi Bel Abbès University, Algeria. He earned his highest diploma in Habilitation in Mathematics from Constantine University, Algeria. He is currently an Assistant Professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.
