Asymptotic Analysis and Perturbation TheoryCRC Press, 18.07.2013 - 550 Seiten Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge o |
Inhalt
Chapter 1 Introduction to Asymptotics | 1 |
Chapter 2 Asymptotics of Integrals | 37 |
Chapter 3 Speeding Up Convergence | 111 |
Chapter 4 Differential Equations | 163 |
Chapter 5 Asymptotic Series Solutions for Differential Equation | 207 |
Chapter 6 Difference Equations | 253 |
Chapter 7 Perturbation Theory | 317 |
Chapter 8 WKBJ Theory | 389 |
Chapter 9 MultipleScale Analysis | 443 |
Guide to the Special Functions | 479 |
Answers to OddNumberedProblems | 495 |
Bibliography | 519 |
Back Cover | 521 |
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Häufige Begriffe und Wortgruppen
A₁ Airy functions an+1 an+2 analytic arbitrary constant assume asymptotic approximation asymptotic series Borel sum boundary layer C₁ coefficients composite approximation compute continued fraction continued fraction representation cos(t cos(x determine difference equation differential equation divergent eigenvalue endpoints exact solution example expansion expressed FIGURE find the asymptotic Find the leading Frobenius series full asymptotic gamma function gives graph Hence homogeneous equation inhomogeneous initial conditions inner solution integral leading behavior leading order ln(x logarithm Maclaurin series method non-zero order WKBJ outer solution Padé perturbation problem perturbation series Plugging polynomial produce radius of convergence recursion formula regular singular point Richardson extrapolation second order secular terms series solution Shanks transformation shows sin(t sin(x solve Stieltjes strained coordinate subdominant substitution Taylor series theorem valid value problem WKBJ approximation x²y Y₁ Ycomp Ycomp,1 yWKBJ αο