Checking date: 14/04/2023

Course: 2023/2024

Perturbation Methods
Máster Universitario en Matemática Industrial (RD 1393/2007) (Plan: 330 - Estudio: 258)


Department assigned to the subject: Mathematics Department

Type: Electives
ECTS Credits: 6.0 ECTS


LEARNING RESULTS - Recognize and classify a singular or regular problem. - Understand and use the concepts of distinguished limit, dominant balance and scaling. - Understand and use elementary methods to approximate integrals. - Understand and use boundary layer and matched asymptotic expansion methods for ODEs. - Use métodos de escalas múltiples for linear and nonlinear oscillator problems. - Understand and use the Chapman-Enskog method.
Description of contents: programme
- Basic notione of asymptotic analysis. - Approximation of integrals. - Solvability condition for a non-homogeneous linear problem. - Eigenvalue problems. - Poincaré-Linstedt method. - Scaling of singular perturbation problems. - Boundary layer and asymptotic matching. - Method of matched asymptotic expansions. - Method of multiple scales. - Chapman-Enskog method. - Realistic examples in science and engineering
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Calendar of Continuous assessment
Basic Bibliography
  • C.A. Bender, S.A. Orszag. Advanced mathematical methods for scientists and engineers. Addison Wesley. 1978
  • E.J. Hinch. Perturbation Methods. Cambridge U.P.. 1991
  • J. Kevorkian, J. Cole. Multiple Scale and Singular Perturbation Methods. Springer. 1996
  • L.L. Bonilla, M. Carretero. Perturbaciones singulares. copyred. 2009
  • L.L. Bonilla, M. Carretero. Perturbaciones singulares. copyred. 2009
Additional Bibliography
  • A. H. Nayfeh. Introduction to Perturbation Techniques. Wiley. 1981
  • G. B. Whitham . Linear and nonlinear waves. Wiley. 1974
  • J. C. Neu. Singular Perturbations in the Physical Sciences. American Mathematical Society. 2015
  • L. L. Bonilla, S. W. Teitsworth. Nonlinear wave methods for charge transport. Wiley-VCH. 2010
  • M. van Dyke. Perturbation methods in Fluid Mechanics. Parabolic Press. 1975
  • P.A. Lagerstrom. Matched asymptotic expansions. Springer. 1988

The course syllabus may change due academic events or other reasons.