Matching A writeup on formal matching. Figures are not included.

Boundary Value Problem Existence Theorems A writeup summarizing some existence theorems for 2-point boundary value problems.

Averaging A short writeup on transformations to standard form, averaging techniques and a theorem on averaging.

Homework Assignments

• Homework 1 in PDF format Introductory Asymptotics
• Homework 2 in PDF format Regular Expansions
• Homework 3 in PDF format Matched Asymptotics and BVP
• Homework 4 in PDF format Matched Asymptotics and Interior Layers
• Homework 5 in PDF format Lindstedt's Method and Multiple Scales Averaging (should be + instead of - in answer of 3)
• Homework 6 in PDF format Multiple scales for oscillatory systems, general straining and the Method of averaging.
• Homework 7 in PDF format Eigenvalues for elliptic problems with perturbed domains.

Regular_Algebraic.mw Finds the N-th order regular expansion for the solution of a single scalar algebraic equation. (Maple V Release 9). A PDF file of an example can be downloaded here

Regular_BVP.ms Finds the N-th oder regular expansion for the solution of a two-point Boundary Value Problem with Dirchlet boundary conditions. (Maple V Release 9). A PDF file of an example can be downloaded here

Matched_BVP.ms Finds the N-th oder regular expansion for the solution of a two-point Boundary Value Problem with Dirchlet boundary conditions. (Maple V Release 9). A PDF file of an example can be downloaded here

Lindstedt.mws Uses Lindstedt's method for computing an N-th order expansion for the periodic solution of a 2nd order weakly nonlinear problem. (Maple V Release 9). A PDF file of an example can be downloaded here

FixedPeriodStrain.mws Uses fixed period straining in a two-variable expansion to compute leading slowly varying amplitude and phase of a solution which is asymptotic for t=O(e^-1) (Maple V Release 9). A PDF file of an example can be downloaded here

Averaging.mws Uses fixed period straining in a two-variable expansion to compute leading slowly varying amplitude and phase of a solution which is asymptotic for t=O(e^-1) (Maple V Release 9). A PDF file of an example can be downloaded here