Ebook: Second Course in Ordinary Differential Equations for Scientists and Engineers

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.

---

This book fills the need for a junior-senior level book on the more advanced topics of differential equations. It attempts to blend mathematical theory with nontrivial applications from various disciplines. It does not contain lengthy proofs of mathematical theorems. In each case, examples are shown to support theorems and their practical use, and in some cases an "intuitive proof" is included. A wide range of topics is included to afford flexibility if used for a course.

---

This book fills the need for a junior-senior level book on the more advanced topics of differential equations. It attempts to blend mathematical theory with nontrivial applications from various disciplines. It does not contain lengthy proofs of mathematical theorems. In each case, examples are shown to support theorems and their practical use, and in some cases an "intuitive proof" is included. A wide range of topics is included to afford flexibility if used for a course.
Content:
Front Matter....Pages i-xi
Review....Pages 1-16
Boundary Value Problems....Pages 17-59
Special Functions....Pages 60-130
Systems of Ordinary Differential Equations....Pages 131-168
Applications of Symmetry Principles to Differential Equations....Pages 169-209
Equations with Periodic Coefficients....Pages 210-227
Greens’s Functions....Pages 228-262
Perturbation Theory....Pages 263-307
Phase Diagrams and Stability....Pages 308-355
Catastrophes and Bifurcations....Pages 356-400
Sturmian Theory....Pages 401-433
Back Matter....Pages 435-441

---

This book fills the need for a junior-senior level book on the more advanced topics of differential equations. It attempts to blend mathematical theory with nontrivial applications from various disciplines. It does not contain lengthy proofs of mathematical theorems. In each case, examples are shown to support theorems and their practical use, and in some cases an "intuitive proof" is included. A wide range of topics is included to afford flexibility if used for a course.
Content:
Front Matter....Pages i-xi
Review....Pages 1-16
Boundary Value Problems....Pages 17-59
Special Functions....Pages 60-130
Systems of Ordinary Differential Equations....Pages 131-168
Applications of Symmetry Principles to Differential Equations....Pages 169-209
Equations with Periodic Coefficients....Pages 210-227
Greens’s Functions....Pages 228-262
Perturbation Theory....Pages 263-307
Phase Diagrams and Stability....Pages 308-355
Catastrophes and Bifurcations....Pages 356-400
Sturmian Theory....Pages 401-433
Back Matter....Pages 435-441
....