Foundations of Perturbation Methods

Motivation and Philosophy
•    Why perturbation methods are useful: scale separation, decomposition into leading-order and corrective effects, identification of dominant physical mechanisms • 
•    Perturbation vs. numerical approaches: insight, structure, and limitations 
Regular Perturbation Methods 
•    Identification of small parameters 
•    Asymptotic expansions and ordering 
•    Leading-order and first-order corrections
•    Validity and breakdown of regular expansions 
Illustrative Example 
•    Simple elasticity problem with weak material inhomogeneity

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