Differential Equations

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Christian Constanda

   Pages 1-13

3. First-Order Equations

   • Christian Constanda

   Pages 15-42

4. Mathematical Models with First-Order Equations

   • Christian Constanda

   Pages 43-61

5. Linear Second-Order Equations

   • Christian Constanda

   Pages 63-104

6. Mathematical Models with Second-Order Equations

   • Christian Constanda

   Pages 105-117

7. Higher-Order Linear Equations

   • Christian Constanda

   Pages 119-138

8. Systems of Differential Equations

   • Christian Constanda

   Pages 139-187

9. The Laplace Transformation

   • Christian Constanda

   Pages 189-220

10. Series Solutions

    • Christian Constanda

    Pages 221-245

11. Numerical Methods

    • Christian Constanda

    Pages 247-258

12. Back Matter

    Pages 259-297

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This textbook is designed with the needs of today’s student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians. This book is accessible to anyone who has a basic knowledge of precalculus algebra and differential and integral calculus. Its carefully crafted text adopts a concise, simple, no-frills approach to differential equations, which helps students acquire a solid experience in many classical solution techniques. With a lighter accent on the physical interpretation of the results, a more manageable page count than comparable texts, a highly readable style, and over 1000 exercises designed to be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct yet fully rigorous fashion. Apart from several other enhancements, the second edition contains one new chapter on numerical methods of solution.

The book formally splits the "pure" and "applied" parts of the contents by placing the discussion of selected mathematical models in separate chapters. At the end of most of the 246 worked examples, the author provides the commands in Mathematica® for verifying the results. The book can be used independently by the average student to learn the fundamentals of the subject, while those interested in pursuing more advanced material can regard it as an easily taken first step on the way to the next level. Additionally, practitioners who encounter differential equations in their professional work will find this text to be a convenient source of reference.

• differential equations textbook
• numerical methods
• Runge-Kutta method
• multistep methods
• undergraduate differential equations
• differential equations engineers

• Department of Mathematics, The University of Tulsa, Tulsa, USA

  Christian Constanda

Christian Constanda, MS, PhD, DSc, is the holder of the Charles W. Oliphant Endowed Chair in Mathematical Sciences at the University of Tulsa, USA. He is also the Chairman of the International Consortium on Integral Methods in Science and Engineering (IMSE).Other Springer publications by Christian Constanda: Dude, Can you Count? ISBN: 978-1-84882-538-3; (with D. Doty and W. Hamill) Boundary Integral Equation Methods and Numerical Solutions ISBN: 978-3-319-26307-6; Mathematical Methods for Elastic Plates ISBN: 978-1-4471-6433-3; (with G.R. Thomson) Stationary Oscillations of Elastic Plates, ISBN: 978-0-8176-8340-8.

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