Sochacki J., Tongen A. Applying Power Series to Differential Equations: An Exploration through Questions and Projects

Springer, 2023. — 219 p. — (Problem Books in Mathematics). — ISBN 3031245865.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.Preface.
Acknowledgment.
Introduction.
Egg 1: The Quadratic Ordinary Differential Equation.
Egg 2: A First Order Differential Equation with Exponent.
Egg 3: The First Order Sine Differential Equation.
Egg 4: A Second Order ODE with Exponent.
Egg 5: The Second Order Sine ODE—The Single Pendulum.
Egg 6: Newton’s Method and the Steepest Descent Method.
Egg 7: Determining Power Series for Functions Through ODEs.
Egg 8: The Periodic Planar ODE.
Egg 9: The Complex Planar Quadratic ODE.
Egg 10: Newton’s N -Body Problem.
Egg 11: ODEs and Conservation Laws.
Egg 12: Delay Differential Equations.
An Overview of Polynomial ODEs.
A A Review of Maclaurin Polynomials and Power Series.
B The Dog Rabbit Chasing Problem.
C A PDE Example: Burgers’ Equation.
References.True PDF