Asymptotic and Perturbation Methods in Applied
Asymptotic and Perturbation Methods in Applied Mathematics
ESAM 420-1
Fall 2002
Prof. H. Riecke
Suggested Textbooks
- M.H. Holmes, Introduction to Perturbation Methods, Springer, 1995
- C.M. Bender & S.A. Orszag Advanced Mathematical Methods for Scientists and Engineers,
McGraw Hill, 1978
Other Books
- E.J. Hinch, Perturbation Methods, Cambridge University Press,
1991
- J. Kevorkian & J.D. Cole, Multiple Scale and Singular Perturbation Methods, Springer, 1996
- P.A. Lagerstrom, Matched Asymptotic Expansion: Ideas and Techniques, Springer, 1988
- A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley, 1981, 1993
Perturbation Techniques, Wiley, 1973
- M. van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, 1975
Topics to be covered:
- Perturbation methods for algebraic equations
- Explorative examples
regular vs. singular perturbations
- Asymptotic approximation
order ( O, o), gauge functions, uniformity,
transcendentally small terms, manipulating asymptotic expansions,
asymptotic series and convergence
- Regular perturbation problems
- Projectile problem
- Plane Couette flow with variable viscosity
- Electrial potential of slightly perturbed sphere
- Singular perturbations
- Small-mass harmonic oscillator
regular perturbation (weak damping)
singular perturbation (small mass), inner and outer expansion, matching
- Composite expansion
- van Dyke's asymptotic matching principle
- Boundary-value problem
- General linear equation with variable coefficients
- Coefficient non-zero
- Coefficient vanishes at boundary
- Coefficient vanishes inside domain. Turning point
internal layers, no unique solution from matching
- Boundary-layer problem involving lne
- multiple deck
- nonlinear problem
- a slider bearing
- model example for Stokes-Oseen problem
- viscous flow past a sphere
- a combustion problem
- premixed flame propagation
- beam string
- multiple solutions
- Method of strained coordinates
- flow past an air foil
- weakly nonlinear oscillator
- Poincaré-Lindstedt method
- Poincaré-Lighthill-Kuo (PLK) method
- pendulum
- Rayleigh equation. van der Pol oscillator
- Floquet theory. 2nd-order linear equations
- Mathieu equation
The class will continue with 420-2,3 to be taught by Moshe Matalon.
Assignments:
HW 1 PS HTML PDF
HW 2 PS PDF
HW 3 PS PDF
Solutions for HW 3:
1
2
3
4
5
6
7
8
9
problem 3 PS
problem 3 PDF
HW 4 PS PDF
Solutions Problem 2
Midterm PS PDF
Solutions part 1 part 2 part 3
HW 5 PS PDF
Solutions Problem 1 Problem 2
Problem 3
Problem 4
Final: PS PDF
If your browser does not show the html-file HW/appropriately you may tune it by following these
instructions
Office Hours: Mo Tu Th 5-6 in
L550
There will be a take-home midterm and a take-home final.
Homework will be assigned and handed in. Unfortunately, I cannot grade the assignments
in detail.
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On 25 Sep 2002, 22:32.