國立高雄大學圖資館 |

Language: English

Back

Applying power series to differential equationsan exploration through questions and projects /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Applying power series to differential equationsby James Sochacki, Anthony Tongen.
Reminder of title:	an exploration through questions and projects /
Author:	Sochacki, James.
other author:	Tongen, Anthony.
Published:	Cham :Springer International Publishing :2022.
Description:	xii, 217 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations.
Online resource:	https://doi.org/10.1007/978-3-031-24587-9
ISBN:	9783031245879$q(electronic bk.)

Applying power series to differential equationsan exploration through questions and projects /
Sochacki, James.

Applying power series to differential equationsan exploration through questions and projects /[electronic resource] :by James Sochacki, Anthony Tongen. - Cham :Springer International Publishing :2022. - xii, 217 p. :ill., digital ;24 cm. - Problem books in mathematics,2197-8506. - Problem books in mathematics..

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.

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.

ISBN: 9783031245879$q(electronic bk.)

Standard No.: 10.1007/978-3-031-24587-9doiSubjects--Topical Terms:

183925
Differential equations.

LC Class. No.: QA371 / .S63 2022

Dewey Class. No.: 515.35

Applying power series to differential equationsan exploration through questions and projects /
LDR:02884nmm a2200337 a 4500 001 634583
003 DE-He213
005 20230315140522.0
006 m d
007 cr nn 008maaau
008 230529s2022 sz s 0 eng d
020 $a 9783031245879$q(electronic bk.)
020 $a 9783031245862$q(paper)
024 7 $a 10.1007/978-3-031-24587-9 $2 doi
035 $a 978-3-031-24587-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371 $b .S63 2022
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA371 $b .S678 2022
100 1 $a Sochacki, James. $3 941030
245 1 0 $a Applying power series to differential equations $h [electronic resource] : $b an exploration through questions and projects / $c by James Sochacki, Anthony Tongen.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xii, 217 p. : $b ill., digital ; $c 24 cm.
490 1 $a Problem books in mathematics, $x 2197-8506
505 0 $a 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.
520 $a 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.
650 0 $a Differential equations. $3 183925
650 0 $a Power series. $3 468018
650 1 4 $a Differential Equations. $3 285983
650 2 4 $a Sequences, Series, Summability. $3 275704
650 2 4 $a Applied Dynamical Systems. $3 913436
650 2 4 $a Field Theory and Polynomials. $3 274058
700 1 $a Tongen, Anthony. $3 941031
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Problem books in mathematics. $3 573108
856 4 0 $u https://doi.org/10.1007/978-3-031-24587-9
950 $a Mathematics and Statistics (SpringerNature-11649)