Perturbation Methods
I
Course Outline
Assignments
Problem Set I
Preliminary Concepts and Gauge Functions
Problem Set II
Proper Scaling and Regular Perturbations
Problem Set III
Transcendental Equations and Successive Approximations
Problem Set IV
Singular Perturbations, Lindstedt's Technique
Problem Set V
Method of Strained Coordinates, PLK and Pritulo
Problem Set VI
Boundary Layers and Matched Asymptotic Expansions
Problem Set VII
Method of Multiple Scales
Handouts
Formularies
Essential
s
eries
e
xpansions
Essential
t
rigonometric
i
dentities
Solutions to
1st and 2nd order
ODEs
Classification of damped oscillation
s
Classification of regular and singular perturbations by Milton Van Dyke
Special Notes
Class notes (acquired by a fellow student)
Introduction, gauge functions and asymptotic expansions
Finding roots of polynomials
Perturbation techniques for ODEs --Tzitzouris
Boundary layer problems with constant coefficients
Boundary layer problems with variable coefficients
Strained coordinates, Duffing's equation, linear oscillator
Multiple scales
Historical
Contributors
Von Karman's approach to research--as described by Bill Sears
Ludwig Prandtl
Leonhard Euler
Blaise Pascal
and
René Descartes
Isaac Newton
Other contributors
Other
Course notebook
Interesting video titles
Expanding websites
Basic terms
Wolfram Alpha