Abstract
We will use the conventional order symbols as a mathematical measure of the relative order of magnitude of various quantities. Although generalizations are straightforward, we need only be concerned with scalar functions of real variables. In the definitions which follow φ, ψ, etc. are scalar functions of the variable x (which may be a vector) and the scalar parameter ε. The variable x ranges over some domain D and ε belongs to some interval I.
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References
A. Erdelyi, Asymptotic Expansions, Dover Publications, New York, 1956.
G. F. Carrier. M. Krook and C. E. Pearson, Functions of a Complex Variable, Theory and Technique, McGraw-Hill Book Company, New York, 1966.
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© 1981 Springer-Verlag Berlin Heidelberg
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Kevorkian, J., Cole, J.D. (1981). Introduction. In: Perturbation Methods in Applied Mathematics. Applied Mathematical Sciences, vol 34. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4213-8_1
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DOI: https://doi.org/10.1007/978-1-4757-4213-8_1
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