1st Edition

Multiplicative Differential Equations Volume I

By Svetlin G. Georgiev, Khaled Zennir Copyright 2023
380 Pages 5 B/W Illustrations
by Chapman & Hall

380 Pages 5 B/W Illustrations
by Chapman & Hall

Also available as eBook on:

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 uniqueness 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.

Preface

1. Introduction
1. Definition of MDE
2. Order of MDE
3. Solution of MDE
4. Classification of MDE
5. Basic Problems for MDE

2. Elementary First Order MDEs
1. Separable First Order MDEs
2. Multiplicative Homogeneous Functions
3. Multiplicative Homogeneous MDE
4. Exact Multiplicative Differential Equations
5. Multiplicative Integrating Factor

3. First Order Multiplicative Linear Differential Equations
1. Definition. General Solutions
2. The Multiplicative Bernoulli Equation
3. The Multiplicative Riccati Equation
4. Applications
5. Multiplicative Initial Value Problems
6. Some Multiplicative Nonlinear Differential Equations

4.  Second Order Linear MDEs

1. General Properties
2. Multiplicative Linear Dependence
3. The Multiplicative Abel Theorem
4. A Particular Case
5. The Multiplicative Constant Case
6. The Method of Variation of Parameters
7. The Multiplicative Cauchy-Euler Equation

5.  Existence and Uniqueness of Solutions

1. Introduction
2. The Multiplicative Gronwall Type Integral Inequalities
3. Picard’s Method of Successive Approximations and Existence Theorems
4. Uniqueness
5. Continuous Dependence on Initial Data