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

- Explorative examples
- 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

- Small-mass harmonic oscillator
- 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. 2
^{nd}-order linear equations- Mathieu equation

The class will continue with 420-2,3 to be taught by Moshe Matalon.

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.

File translated from T

On 25 Sep 2002, 22:32.