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- Ibragimov, Nail H.
(författare)
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A practical course in differential equations and mathematical modeling
- 2009
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- A practical course in differential equations and mathematical modelling is a unique blend of the traditional methods with Lie group analysis enriched by author’s own theoretical developments. The main objective of the book is to develop new mathematical curricula based on symmetry and invariance principles. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on author’s long-term experience of teaching at Novosibirsk and Moscow Universities in Russia, Collège de France, Georgia Tech and Stanford University in USA, Universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares the students for solving modern nonlinear problems and attracts essentially more students than the traditional way of teaching mathematics. The book can be used as a main textbook by undergraduate and graduate students and their teachers in applied mathematics, physics and engineering sciences.
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| 5. |
- Ibragimov, Nail H., et al.
(författare)
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Applications of Lie group analysis in Geophysical fluid dynamics
- 2011
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book introduces an effective method for seeking local and nonlocal conservation laws and exact solutions for nonlinear two-dimensional equations which provide a basic model in describing internal waves in the ocean. The model consists of non-hydrostatic equations of motion which uses the Boussinesq approximation and linear stratification. The Lie group analysis is used for constructing non-trivial conservation laws and group invariant solutions. It is shown that nonlinear equations in question have remarkable property to be self-adjoint. This property is crucial for constructing physically relevant conservation laws for nonlinear internal waves in the ocean. The comparison with the previous analytic studies and experimental observations confirrms that the anisotropic nature of the wave motion allows to associate some of the obtained invariant solutions with uni-directional internal wave beams propagating through the medium. Analytic examples of the latitude-dependent invariant solutions associated with internal gravity wave beams are considered. The behavior of the invariant solutions near the critical latitude is investigated.
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| 6. |
- Ibragimov, Nail H., et al.
(författare)
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Approximate and renormgroup symmetries
- 2009
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Approximate and Renormgroup Symmetries deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self contained introduction to basic concepts and methods of Lie group analysis, and provides an easy to follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics --mathematicians and nonmathematicians--interested in methods of applied group analysis for investigating nonlinear problems in physical, engineering and natural sciences.
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| 7. |
- Ibragimov, Nail H., et al.
(författare)
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Approximate groups and renormgroup symmetries
- 2008
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- The book deals with so-called renormalization group symmetries considered in the framework of approximate transformation groups. Renormgroup symmetries provide a basis for the renormgroup algorithm for improving solutions to boundary value problems by converting "less applicable solutions" into "more applicable solutions". the algorithm is particularly useful for improving approximate solutions given by the perturbation theory.
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| 8. |
- Ibragimov, Nail H.
(författare)
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Approximate transformation groups
- 2008
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- These notes provide an easy to follow introduction to the topic and are based on my talks at various conferences, in particular on the plenary lecture at the International Workshop on ``Differential equations and chaos" (University of Witwatersrand, Johannesburg, South Africa, January 1996). The book is prepared for the new graduate course ``Approximate transformation groups" that will be given at Blekinge Institute of Technology during January-March, 2009.
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| 9. |
- Ibragimov, Nail H.
(författare)
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Differentialekvationer och matematisk modellering
- 2009
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Differentialekvationer och matematisk modellering" är avsedd för högskolestuderande på nybörjarnivå, exempelvis inom ingenjörs- och naturvetarprogram. Den kombinerar klassiska lösningsmetoder med moderna metoder från gruppanalys. Texten är generös med exempel och övningsuppgifter, vissa med fullständiga lösningar. Många vanliga läroböcker är begränsade till ett antal speciella differentialekvationer som man råkar kunna lösa med enkla recept. De flesta matematiska modeller inom naturvetenskap och teknik leder dock till ickelinjära differentialekvationer som man inte kan lösa med traditionella metoder. Med de redskap som ges i denna bok ligger många intressanta tillämpningar inom räckhåll.
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| 10. |
- Ibragimov, Nail H., et al.
(författare)
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Introduction to differential equations
- 2006
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book is based on lectures in differential equations delivered by the authors, namely, by A. Al-Hammadi at the University of Bahrain and by N. Ibragimov at the Blekinge Institute of Technology, Sweden. It is designed for a one semester course in differential equations. We assume that the reader has taken standard courses in mathematical analysis and has encountered basic concepts from linear algebra such as vectors, matrices and algebraic linear systems. Our aim is to provide students with an easy to follow introduction to the subject containing classical devices enriched by fundamentals of Lie group methods given in Chapter 9.
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