Starts 5 May 2025 10:00
Ends 16 May 2025 19:00
Africa/Bamako
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PWF Mali: Course on Ordinary Differential Equations Using Green’s Function
Faculty of Sciences and Techniques, University of Sciences, Techniques and Technologies of Bamako (USTTB), Mali
The course in mathematical methods for physics is mandatory for the Master’s programme in theoretical physics. The course on ordinary differential equations (ODEs) using Green’s function complements the course on mathematical methods in physics coordinated by Dr. Kaniba Mady KEITA, the local organizer of the present project.
The course is about solving non-homogeneous linear second-order ordinary differential equations, with given boundary conditions, by the method of Green’s functions. This method can be easily generalized to problems where the method of variation of constants fails. Green’s functions play a very important role in mathematics and in theoretical physics. They can be used to reduce the eigenvalue problem associated with a differential operator to the more tractable eigenvalue problem for an integral operator.
The duration of the activity is 30 hours and is scheduled for the same period as other courses of the Master’s programme in Physics. The programme of the activity includes 08 hours of tutorial and discussion sessions, 02 hours of a session about careers and opportunities in mathematical physics, and a compulsory examination.
Course content
35 students formally registered for the first year and the second year Master’s programme in Physics, 2024–2025, at the Faculty of Sciences and Techniques, University of Sciences, Techniques and Technologies of Bamako (USTTB), Mali.
SPEAKER:
Dr. Laure GOUBA, International Centre for Theoretical Physics (ICTP), Trieste, Italy.
LOCAL COORDINATOR:
Dr. Kaniba Mady KEITA
Faculty of Sciences and Techniques, University of Sciences, Techniques and Technologies of Bamako (USTTB), Mali.
The course is about solving non-homogeneous linear second-order ordinary differential equations, with given boundary conditions, by the method of Green’s functions. This method can be easily generalized to problems where the method of variation of constants fails. Green’s functions play a very important role in mathematics and in theoretical physics. They can be used to reduce the eigenvalue problem associated with a differential operator to the more tractable eigenvalue problem for an integral operator.
The duration of the activity is 30 hours and is scheduled for the same period as other courses of the Master’s programme in Physics. The programme of the activity includes 08 hours of tutorial and discussion sessions, 02 hours of a session about careers and opportunities in mathematical physics, and a compulsory examination.
Course content
- Generalities;
- Integral and differential operators;
- Second-order self-adjoint operators;
- First-order differential operators;
- Second-order linear differential operators;
- Green’s function;
- Properties of the Green’s functions;
- Construction of the Green’s functions;
- Green’s function method versus the method of variation of constants;
- Green’s functions for in-homogeneous boundary conditions;
- Initial value Green’s functions;
- Generalized Green’s function;
- Series representations of the Green’s function.
35 students formally registered for the first year and the second year Master’s programme in Physics, 2024–2025, at the Faculty of Sciences and Techniques, University of Sciences, Techniques and Technologies of Bamako (USTTB), Mali.
SPEAKER:
Dr. Laure GOUBA, International Centre for Theoretical Physics (ICTP), Trieste, Italy.
LOCAL COORDINATOR:
Dr. Kaniba Mady KEITA
Faculty of Sciences and Techniques, University of Sciences, Techniques and Technologies of Bamako (USTTB), Mali.