Special functions of mathematical physics 1100-FSFM
The course covers basic special functions and their applications to partial differential equations.
Plan of the course
1. Gamma function
2. The saddlepoint method
3. Differential equations in the complex domain and their singularities.
4. Hypergeometric equation and functions.
5. Confluent and Bessel equation and functions.
6. Laplace and Helmholtz equation.
7. Orthogonal polynomials.
8. Classical orthogonal polynomials: Hermite, Laguerre, Jacobi and Legendre.
9. Spherical harmonics.
Student's work load:
Lectures: 30 h -- 2ECTS
Exercise classes 30h -- 2ECTS
Preparation for lectures: 30 h -- 1 ECTS
Preparation for the exam: 30 h -- 1 ECTS
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Knowledge: Familiarity with basic special functions.
Skills: Solving simple problems using the most frequent special functions
Attitude: Appreciation of the beauty, depth and usefulness
of special functions, especially in the context of applications to physics.
Assessment criteria
written and oral exam
Practical placement
does not apply
Bibliography
1. E.T.Whittaker and G.N.Watson: A course of modern analysis, Cambridge Univ. Press 1962
2. J.Dereziński: Lecture notes
https://www.fuw.edu.pl/~derezins/mmf-i.pdf
https://www.fuw.edu.pl/~derezins/spec-func.pdf
https://www.fuw.edu.pl/~derezins/bessel.pdf
https://www.fuw.edu.pl/~derezins/mmf-iii.pdf
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: