Applying Power Series to Differential Equations
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Applying Power Series to Differential Equations
An Exploration through Questions and Projects
Sochacki, James; Tongen, Anthony
Springer International Publishing AG
03/2024
217
Mole
Inglês
9783031245893
15 a 20 dias
Descrição não disponível.
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.
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differential equations;power series;dynamical systems;numerical solutions;polynomials;STEM;numerical approximation;ordinary differential equations;ODE;linear ODE;Poincare-Bendixson theory;Newton's method;Newton's N-Body problem;Maclaurin polynomials
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.
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