Differential Equations: Methods and Applications

1. Front Matter

   Pages i-x

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2. Modelling and Definitions

   • Belkacem Said-Houari

   Pages 1-13

3. First-Order Differential Equations

   • Belkacem Said-Houari

   Pages 15-43

4. Linear Second-Order Equations

   • Belkacem Said-Houari

   Pages 45-88

5. Laplace Transforms

   • Belkacem Said-Houari

   Pages 89-124

6. Power Series Solution

   • Belkacem Said-Houari

   Pages 125-140

7. Systems of Differential Equations

   • Belkacem Said-Houari

   Pages 141-187

8. Qualitative Theory

   • Belkacem Said-Houari

   Pages 189-207

9. Back Matter

   Pages 209-212

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This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.
To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.
The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. 

• First order differential equations
• Second order differential equations
• Laplace transform
• Power series
• Fundamental solution of differential equation
• limit cycle
• ordinary differential equations

The book presents a concise introduction to the theory of ordinary differential equations that arise in the real world, and the methods used to solve them. Each section or chapter of the book has been followed with examples and exercises with detailed solutions. … The book is outstanding and will be excellently suited for students who have completed two semesters of differential and integral calculus and need a concise presentation of an introduction to the theory of ordinary differential equations.” (Olusola Akinyele, zbMATH 1338.34003, 2016)

• Mathematicsand Natural Sciences Dept., Alhosn University, Abu Dhabi, United Arab Emirates

  Belkacem Said-Houari

Dr. Belkacem Said-Houari received his Ph.D degree in partial differential equations (hyperbolic problems and nonclassical thermoelasticity) from Annaba University (Algeria) in 2005.

His research interests focus on analysis of hyperbolic PDE (e.g. in thermoelasticity, Timoshenko systems, nonlinear wave equations), integro-differential equations, parabolic and hyperbolic-parabolic PDE.

He is the author or co-author of 45 research papers published in refereed international journals.

He is the winner of the Abdul Hameed Shoman Award for Young Arab Researchers, Mathematics (2012). 

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