LEADER 04282nam 22007215 450 001 9910682548903321 005 20230526095228.0 010 $a3-031-24587-3 024 7 $a10.1007/978-3-031-24587-9 035 $a(CKB)5580000000524037 035 $a(DE-He213)978-3-031-24587-9 035 $a(EXLCZ)995580000000524037 100 $a20230315d2022 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApplying Power Series to Differential Equations$b[electronic resource] $eAn Exploration through Questions and Projects /$fby James Sochacki, Anthony Tongen 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (XII, 217 p. 45 illus., 36 illus. in color.) 225 1 $aProblem Books in Mathematics,$x2197-8506 311 $a3-031-24586-5 327 $aChapter 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. 330 $aThis book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study. 410 0$aProblem Books in Mathematics,$x2197-8506 606 $aDifferential equations 606 $aSequences (Mathematics) 606 $aDynamics 606 $aNonlinear theories 606 $aAlgebraic fields 606 $aPolynomials 606 $aDifferential Equations 606 $aSequences, Series, Summability 606 $aApplied Dynamical Systems 606 $aField Theory and Polynomials 606 $aEquacions diferencials$2thub 606 $aSuccessions (Matemātica)$2thub 606 $aDināmica$2thub 606 $aTeories no lineals$2thub 608 $aLlibres electrōnics$2thub 615 0$aDifferential equations. 615 0$aSequences (Mathematics). 615 0$aDynamics. 615 0$aNonlinear theories. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 14$aDifferential Equations. 615 24$aSequences, Series, Summability. 615 24$aApplied Dynamical Systems. 615 24$aField Theory and Polynomials. 615 7$aEquacions diferencials 615 7$aSuccessions (Matemātica) 615 7$aDināmica 615 7$aTeories no lineals 676 $a515.35 700 $aSochacki$b James$4aut$4http://id.loc.gov/vocabulary/relators/aut$01351242 702 $aTongen$b Anthony$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910682548903321 996 $aApplying Power Series to Differential Equations$93091240 997 $aUNINA