Università degli Studi di Perugia

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Unit SYMMETRIES IN MATHEMATICAL PHYSICS

Course
Mathematics
Study-unit Code
A001271
Curriculum
Didattico-generale
Teacher
Maria Clara Nucci
Teachers
  • Maria Clara Nucci - Didattica Ufficiale
Hours
  • 42 ore - Didattica Ufficiale - Maria Clara Nucci
CFU
6
Course Regulation
Coorte 2019
Offered
2019/20
Learning activities
Affine/integrativa
Area
Attività formative affini o integrative
Sector
MAT/07
Type of study-unit
Opzionale (Optional)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
ENGLISH
Contents
The program will cover the fundamentals of Lie symmetries for ordinary and partial differential equations. In the case of ordinary differential equations Noether symmetries will be also introduced, and the role of the Jacobi last multiplier and its properties will be emphasized. Since searching for symmetries requires lengthy algebraic manipulations computer REDUCE programs developed by the lecturer will be used, as well as some MAPLE worksheets.
Reference texts
Daniel J. Arrigo, Symmetry Analysis of Differential Equations: An Introduction, John Wiley & Sons, 2015
Peter E. Hydon, Symmetry methods for differential equations: a beginner's guide, Cambridge University Press, 2000
Nail H. Ibragimov, Elementary Lie group analysis and ordinary differential equations, Wiley, 1999
Peter J. Olver , Applications of Lie groups to differential equations, Springer, 1993
Hans Stephani, Differential equations: their solution using symmetries, Cambridge University Press, 1990

The lecturer will supply notes, and scientific articles.
Educational objectives
Being able to apply Lie symmetries and their properties to both ordinary and partial differential equations.
Prerequisites
The basics of Algebra, Rational Mechanics, Analysis I and II, Mathematical Physics I.
Teaching methods
Face-to-face Lectures and practical training in the Computer Lab. Office hours.
Learning verification modality
Oral exam with a detailed presentation of the student's report on her/his own project that is assigned the last day of class; the student must also show to be able to use REDUCE and MAPLE for the purpose.
Extended program
The detailed program can be seen here:
http://www.dmi.unipg.it/nucci/SMMprog16_17.pdf
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