Applying power series to differential equations : an exploration through questions and projects / James Sochacki, Anthony Tongen.

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.