COURSE UNIT TITLE

: APPLICATIONS OF LIE GROUPS TO DIFFERENTIAL EQUATIONS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6043 APPLICATIONS OF LIE GROUPS TO DIFFERENTIAL EQUATIONS I ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR BURCU SILINDIR YANTIR

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The objective is to study the basic concepts of lie group analysis, symmetry groups of ODEs and application of Lie group theory to the solution of ODEs.

Learning Outcomes of the Course Unit

1   Will be able to know the terminology in group analysis of differential equations.
2   Will be able to apply dimensional analysis to differential equations.
3   Will be able to use basic symmetry methods for solving ODEs.
4   Will be able to write an explicit algorithm to find one parameter Lie group of point transformations of a given ODE.
5   Will be able to reduce of order of ODEs under multiparameter Lie groups of point transformations.
6   Will be able to wirite determining equations for integrating factors of third and higher order ODEs.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Dimensional analysis and its applications to PDEs
2 Generalization of dimensional analysis
3 Lie groups of transformations, Infinitesimal transformations
4 Point transformations and extended transformations
5 Multiparameter Lie groups of transformations and Lie algebras
6 Mappings of curves and surfaces, Local transformations
7 First order ODEs
8 Invariance of second order ODEs under point symmetries
9 Examples of third and higher order ODEs
10 Reduction of order of ODEs under multiparameter Lie groups of point transformations
11 Contact symmetries and higher order symmetries
12 First order ODEs, Determing equations for integrating factors of second order ODEs, First integrals of second order ODEs
13 First integrals of second order ODEs.
14 Determining equations for integrating factors of third and higher order ODEs

Recomended or Required Reading

Textbook:
1. George Bluman and Stephen Anco, Symmetry and Integration Methods for Differential Equations, 2nd ed., Springer, 2010, ISBN-13: 978-1441931474
Supplementary Book(s):
2. L. Dresner, Applications of Lie s Theory of Ordinary and Partial Differential Equations, Taylor & Francis, 1998, ISBN-13: 978-0750305310
3. Peter J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Springer, 2010, ISBN-13: 978-0387950006
4. Nail H. Ibragimov, A Practical Course in Differential Equations and Mathematical Modelling: classical and new methods, nonlinear mathematical models, symmetry and invariance principles, World Scientific Publishing Compony, 2009, ISBN-13: 978-9814291941

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 PRS PRESENTATION
3 FCG FINAL COURSE GRADE ASG * 0.50 + PRS * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

The assessment will be executed based on the mean of the grades.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

e-mail: burcu.silindir@deu.edu.tr
Office: (232) 301 8590

Office Hours

Will be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 3 42
Preparing presentations 1 50 50
Project Preparation 1 50 50
Project Assignment 1 5 5
Project Final Presentation 1 5 5
TOTAL WORKLOAD (hours) 194

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1444545443
LO.244343343
LO.33344444443
LO.44434434343
LO.54434434443
LO.64434434443

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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