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Mathematical methods of physics

General data

Course ID: WM-CH-MMF
Erasmus code / ISCED: (unknown) / (unknown)
Course title: Mathematical methods of physics
Name in Polish: Metody matematyczne fizyki
Organizational unit: Faculty of Mathematics and Natural Sciences. School of Exact Sciences.
Course groups:
Course homepage: http://pracownicy.uksw.edu.pl/mwolf/MMF/
ECTS credit allocation (and other scores): 6.00 Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.
Language: Polish
(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się:

physical sciences
Subject level:

advanced
Learning outcome code/codes:

K_W01 23

K_U01 32

K_K01 11
Short description:

For theoreticians.
Full description:

1. Analytic function. Evaluation of integrals with help of residua.

2. Calculus of variations.

3. Fourier transform.

4. Dirac's delta function.

5. Generalized functions (distributions).

6. Hilbert's spaces. Base. Polarisation formula.

7. Linear operators. Norm of operators.

8. Self-adjoint operators. Spectral theorem.

9. Unitary operators. Stone’s Theorem.

10, Eigenvalue problems for self-adjoint operators.

11. Complete orthonormal sets of functions. Hermite'a, Laguerre and Lagranges polynomials.

12. Green's functions.

13. Potential theory.

14. Group theory and their representations,

15. Applications of group theory in physics.
Bibliography:

1. Frederick W. Byron, Robert W. Fuller, Mathematics of classical and quantum physics, Dover Publications, Year: 1992

2. K.Maurin, Methods of Hilbert spaces. PWN, Warszawa, 1962

3. Halmos P.R. A Hilbert Space Problem Book, Springer, kilka wydań

Literatura uzupełniająca:

1. R. Penrose, Droga do rzeczywistości. Wyczerpujący przewodnik po prawach rządzą-cych Wszechświatem, Warszawa, Prószyński i s-ka, 2006, II wyd. 2011

2. Miesięcznik Delta: http://www.deltami.edu.pl/
Efekty kształcenia i opis ECTS:

Egzamin. Weryfikacja wykazuje, że bez uchwytnych niedociągnięć ma wiedzę na temat podstaw przestrzeni wektorowych

oraz

przestrzeni Hilberta oraz teorii grup
Assessment methods and assessment criteria:

Egzamin. Weryfikacja wykazuje, że bez uchwytnych niedociągnięć ma wiedzę na temat podstaw przestrzeni wektorowych oraz

przestrzeni Hilberta oraz teorii grup.

Classes in period "Summer semester 2021/22" (past)

Time span: 2022-02-01 - 2022-06-30
Selected timetable range:
Navigate to timetable
Type of class:
Classes, 30 hours more information
Lectures, 30 hours more information
Coordinators: (unknown)
Group instructors: (unknown)
Students list: (inaccessible to you)
Examination: examination
(in Polish) E-Learning:

(in Polish) E-Learning (pełny kurs) z podziałem na grupy
Type of subject:

obligatory
(in Polish) Grupa przedmiotów ogólnouczenianych:

(in Polish) nie dotyczy

Classes in period "Summer semester 2022/23" (past)

Time span: 2023-02-01 - 2023-06-30
Selected timetable range:
Navigate to timetable
Type of class:
Classes, 30 hours more information
Lectures, 30 hours more information
Coordinators: Marek Wolf
Group instructors: Marek Wolf
Students list: (inaccessible to you)
Examination: examination
(in Polish) E-Learning:

(in Polish) E-Learning (pełny kurs) z podziałem na grupy
Type of subject:

obligatory
(in Polish) Grupa przedmiotów ogólnouczenianych:

(in Polish) nie dotyczy

Classes in period "Summer semester 2023/24" (in progress)

Time span: 2024-02-15 - 2024-06-30
Selected timetable range:
Navigate to timetable
Type of class:
Classes, 30 hours more information
Lectures, 30 hours more information
Coordinators: Marek Wolf
Group instructors: Marek Wolf
Course homepage: http://pracownicy.uksw.edu.pl/mwolf/MMF/
Students list: (inaccessible to you)
Examination: examination
(in Polish) E-Learning:

(in Polish) E-Learning
(in Polish) Opis nakładu pracy studenta w ECTS:

I have no idea
Type of subject:

obligatory
(in Polish) Grupa przedmiotów ogólnouczenianych:

(in Polish) nie dotyczy
Short description:

Lectures for theoretical physicists
Full description:

1. Complex a2. Variational calculunalysis. Caculating integrals with residues.

2. Variational calculus

3. Fourier transform.

4.Dirac's delta function.

5. Distributions.

6. Hilbert spaces. Base, osthogonal vectors.

7. Linear operators. Spectral theorem.

8. Self-conjugate operators.

9. Unitary operatirs..

10. Eigenvaule problems for self-conjugate operators.

11. Complete setes of functions. Hermite and Laguerre polinomials.

12. Green's functions.

13. Potential theory.

14. Group theory and representaion theory.

1. Applicagtion of group theory in physics.
Bibliography:

1. Frederick W. Byron, Robert W. Fuller, Mathematics of classical and quantum physics, Dover Publications, Year: 1992

2. K.Maurin, Methods of Hilbert spaces. PWN, Warszawa, 1962
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