Introduction to Asymptotic Approximations

  • Mark H. Holmes
Part of the Texts in Applied Mathematics book series (TAM, volume 20)


We will be interested in this book in using what are known as asymptotic expansions to find approximate solutions of differential equations. Usually our efforts will be directed toward constructing the solution of a problem with only occasional regard for the physical situation it represents. However, to start things off, it is worth considering a typical physical problem to illustrate where the mathematical problems originate. A simple example comes from the motion of an object projected radially upward from the surface of the Earth. Letting x(t) denote the height of the object, measured from the surface, from Newton’s second law we obtain the following equation of motion:


Asymptotic Approximation Convergent Asymptotic Expansion Intermediate Expression Swell Power Series Function Semiconvergent Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Mark H. Holmes
    • 1
  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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