Dr. Neil Balmforth
Helpful integrals (in case you missed them in class)
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.
I. Asymptotic series
II. Solution of algebraic systems
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.
E. J. Hinch, ``Perturbation Methods''
C. Bender and S. Orszag, ``Advanced mathematical methods for scientists
Video lectures on Eigenvalue problems:
Snow day notes and matlab codes:
Ass. 1 (first page), due Sep 22
Ass. 1 (second page), due Oct 13
Department of Mathematics / Fluid Labs / Neil Balmforth / Courses