Asymptotic Approximations

  • I. Andrianov
  • J. Awrejcewicz
  • L. I. Manevitch
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


The series generated by a perturbation approach does not necessarily converge. Asymptotic methods use a mathematical apparatus of a somewhat peculiar nature — asymptotic series. They diverge but still approximate the functions in hand in a certain sense. Briefly, we can say that a convergent series represents a function at x = x 0, n → ∞ (Fig. 1.1), while an asymptotic series is valid for n = n 0, xx 0 (Fig. 1.2).


Asymptotic Approximation Main Term Asymptotical Series Integration Interval Dimensional Quantity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • I. Andrianov
    • 1
    • 2
  • J. Awrejcewicz
    • 3
  • L. I. Manevitch
    • 4
  1. 1.KölnGermany
  2. 2.Pridneprovskaya State Academy of Civil Engineering and ArchitectureDnepropetrovkUkraine
  3. 3.Dept. of Automatics and BiomechanicsTechnical University LodzLodzPoland
  4. 4.N. N. Semenov Institute of Chemical Physics RASMoscowRussian Federation

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