Second Course in Ordinary Differential Equations for Scientists and Engineers

1. Front Matter

   Pages i-xi

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2. Review

   • Mayer Humi, William Miller

   Pages 1-16

3. Boundary Value Problems

   • Mayer Humi, William Miller

   Pages 17-59

4. Special Functions

   • Mayer Humi, William Miller

   Pages 60-130

5. Systems of Ordinary Differential Equations

   • Mayer Humi, William Miller

   Pages 131-168

6. Applications of Symmetry Principles to Differential Equations

   • Mayer Humi, William Miller

   Pages 169-209

7. Equations with Periodic Coefficients

   • Mayer Humi, William Miller

   Pages 210-227

8. Greens’s Functions

   • Mayer Humi, William Miller

   Pages 228-262

9. Perturbation Theory

   • Mayer Humi, William Miller

   Pages 263-307

10. Phase Diagrams and Stability

    • Mayer Humi, William Miller

    Pages 308-355

11. Catastrophes and Bifurcations

    • Mayer Humi, William Miller

    Pages 356-400

12. Sturmian Theory

    • Mayer Humi, William Miller

    Pages 401-433

13. Back Matter

    Pages 435-441

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The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a junior-senior level book on the more advanced topics of differential equations. In fact the number of engineering and science students requiring a second course in these topics has been increasing. This book is an outgrowth of such courses taught by us in the last ten years at Worcester Polytechnic Institute. The book attempts to blend mathematical theory with nontrivial applications from varipus disciplines. It does not contain lengthy proofs of mathemati~al theorems as this would be inappropriate for its intended audience. Nevertheless, in each case we motivated these theorems and their practical use through examples and in some cases an "intuitive proof" is included. In view of this approach the book could be used also by aspiring mathematicians who wish to obtain an overview of the more advanced aspects of differential equations and an insight into some of its applications. We have included a wide range of topics in order to afford the instructor the flexibility in designing such a course according to the needs of the students. Therefore, this book contains more than enough material for a one semester course.

• Boundary value problem
• Eigenvalue
• differential equation
• ordinary differential equation
• partial differential equation

• Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, USA

  Mayer Humi, William Miller

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