Dr. Neil Balmforth
COURSES
Perturbation Methods
Exact or numerical techniques are not the only way to
solve problems or understand their solutions.
This course describes the machinery of asymptotic analysis
which can be applied to the solution of physical problems.
The syllabus:
I. Asymptotic series
II. Solution of algebraic systems
III. Integrals
IV. Differential equations
V. Matched asymptotics
VI. Multiple scales
VII. Improvement of series
Special emphasis will be given to applying the techniques to
problems of physical relevance (e.g. analysis
of wave dispersion relations, amplitude expansions for forming patterns,
dynamics of nonlinear oscillators, fluid boundary layers).
Assessment will involve coursework (homework problems) and examination.
Recommended texts:
E. J. Hinch, ``Perturbation Methods''
C. Bender and S. Orszag, ``Advanced mathematical methods for scientists
and engineers''
Assignments
Mathieu problem
Final
