Applying Power Series to Differential Equations

​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.

• 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: Newton’s 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: Newton’s 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.