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In this program

Singular perturbations
Inner/outer expansions
Method of matched asymptotic expansions
WKB theory for linear ODEs with large parameters
Turning points
Connection formulas (overview)
Boundary-layer theory for PDEs (introduction)

Boundary layers and matched asymptotics

Connection formulas (overview)

Asymptotic & perturbation methods · Standard syllabus

Topic

Connection formulas (overview)

Practice by unit: Boundary layers and matched asymptotics

Graduate Asymptotic & Perturbation Methods — scope drawn from open asymptotics notes and typical US graduate asymptotics syllabi.

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