This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.
Chapter
1. Introduction: The Linear ODE: x = bx + c.
Chapter
2. Egg 1:
The Quadratic ODE: x = ax2 + bx + c.
Chapter
3. Egg 2: The First Order
Exponent ODE: x = xr.
Chapter
4. Egg 3: The First Order Sine ODE: x = sin
x.
Chapter
5. Egg 4: The Second Order Exponent ODE: x = xr.
Chapter
6.
Egg 5: The Second Order Sine ODE - The Single Pendulum.
Chapter
7. Egg 6:
Newtons Method and the Steepest Descent Method.
Chapter
8. Egg 7:
Determining Power Series for Functions through ODEs.
Chapter
9. Egg 8: The
Periodic Planar ODE: x = y + ax2 + bxy + cy2 ; y = x + dx2 + exy + fy2.-
Chapter
10. Egg 9: The Complex Planar Quadratic ODE: z = az2 + bz + c.-
Chapter
11. Egg 10: Newtons N-Body Problem.
Chapter
12. Egg 11: ODEs and
Conservation Laws.
Chapter
13. Egg 12: Delay Differential Equations.-
Chapter
14. An Overview of Our Dozen ODEs.-
Chapter
15. Appendix
1. A Review
of Maclaurin Polynomials and Power Series.
Chapter
16. Appendix
2. The Dog
Rabbit Chasing Problem.
Chapter
17. Appendix
3. A PDE Example: Burgers
Equation.- References.
James Sochacki is a Professor Emeritus and Director of the Center for Computational Mathematics and Modeling at James Madison University, USA. Dr. Sochacki holds a PhD in Applied Mathematics (1985) and a Master´s degree (1981) from the University of Wyoming, USA. His research interests lie in initial value ordinary and partial differential equations. Anthony Tongen is a Professor and Vice Provost, Office of Research and Scholarship, at James Madison University, USA. Dr. Tongen holds a PhD in Applied Mathematics (2002) from Northwestern University, USA. His research focuses on mathematical biology, numerical analysis, dynamical systems, and game theory.
