Dr. Neil Balmforth

Perturbation Methods

The final! (due Dec 17th, by the end of the day; you can drop them off in paper form at my office, or email me a pdf)

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.
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''

Video lectures on Eigenvalue problems: I II III

Snow day notes and matlab codes: Notes m550bvp6.m m550x.m

Ass. 1 (first page), due Sep 22
Ass. 2 (second page), due Oct 13
Ass. 3 (third page), due Nov 6
Ass. 4 (fourth page), due Nov 22
Ass. 5 (fifth page), due Dec 8

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