Module also offered within study programmes:
General information:
Name:
Mathematical Methods of Physics
Course of study:
2016/2017
Code:
JFI-3-101-s
Faculty of:
Physics and Applied Computer Science
Study level:
Third-cycle studies
Specialty:
-
Field of study:
Physics
Semester:
1
Profile of education:
Academic (A)
Lecture language:
Polish
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
dr hab. inż. Spisak Bartłomiej (spisak@novell.ftj.agh.edu.pl)
Academic teachers:
dr hab. inż. Wołoszyn Maciej (woloszyn@newton.fis.agh.edu.pl)
dr hab. inż. Spisak Bartłomiej (spisak@novell.ftj.agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Skills
M_U001 Students are capable of using the power-series method for solving 2nd order diff. equations. For moderately complex equations he/she knows how to construct the second solution. Is able to analyse the usefullness of the obtained results in the quantum-mechanical context. FI3A_U01 Activity during classes,
Oral answer,
Participation in a discussion,
Presentation
M_U002 Student knows how to construct representation of a moderately complex function using appropriately chosen orthogonal base.treści problemu fizycznego. FI3A_U01 Activity during classes,
Oral answer,
Participation in a discussion,
Presentation
M_U003 Student is capable of working in a team solving some calculational problems; he/she is capable of presenting a given physical problem in the language of mathematics. Knows how to find in the Internet pages that contain detailed information about the functions of the mathematical physics and prepare on that basis a presentation with the help of the lecturer. FI3A_U01, FI3A_U02 Case study,
Oral answer,
Presentation
Knowledge
M_W001 The student knows the power-series method for solving ordinary, second-ordrer differential equations. He/she identifies the basic equations of physics and canonical forms (Gauss and confluent equations). He/she understands implications of boundary conditions and the origin of quantum-mechanical quantization of observables. FI3A_W01 Activity during classes,
Oral answer,
Participation in a discussion,
Presentation
M_W002 The student understands tthe idea of orthogonal bases in Hilbert spaces. He/she is able of selecting an adequate base for a given type of interval of the x variable and understands the necessity of "translating" the information in the language of the selected base. FI3A_W01 Activity during classes,
Participation in a discussion,
Presentation
M_W003 Students identify the basis types of the partial differential equations of physics and the basic techniques used for solving the (separation of variables, integral transforms) FI3A_W01 Activity during classes,
Oral answer,
Participation in a discussion,
Presentation
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Skills
M_U001 Students are capable of using the power-series method for solving 2nd order diff. equations. For moderately complex equations he/she knows how to construct the second solution. Is able to analyse the usefullness of the obtained results in the quantum-mechanical context. - - - - - + - - - - -
M_U002 Student knows how to construct representation of a moderately complex function using appropriately chosen orthogonal base.treści problemu fizycznego. - - - - - + - - - - -
M_U003 Student is capable of working in a team solving some calculational problems; he/she is capable of presenting a given physical problem in the language of mathematics. Knows how to find in the Internet pages that contain detailed information about the functions of the mathematical physics and prepare on that basis a presentation with the help of the lecturer. - - - - - + - - - - -
Knowledge
M_W001 The student knows the power-series method for solving ordinary, second-ordrer differential equations. He/she identifies the basic equations of physics and canonical forms (Gauss and confluent equations). He/she understands implications of boundary conditions and the origin of quantum-mechanical quantization of observables. + - - - - - - - - - -
M_W002 The student understands tthe idea of orthogonal bases in Hilbert spaces. He/she is able of selecting an adequate base for a given type of interval of the x variable and understands the necessity of "translating" the information in the language of the selected base. + - - - - - - - - - -
M_W003 Students identify the basis types of the partial differential equations of physics and the basic techniques used for solving the (separation of variables, integral transforms) + - - - - - - - - - -
Module content
Lectures:

Curvilinear reference systems;
Quantum-mechanics operators Lz i L2 in spherical and cylindrical coordinate systems.
Partial differential equations of classical and quantum physics.
The method of variable separation (Laplace equation in polar spherical system – detailed disscusion)
2nd order linear differential equations (1 variable).
The method of Frobenius (power series).
Gauss (hypergeometric) equation; confluent equation.
Truncated series (Legendre equation).
Applications:
Schroedinger equation for hydrogen atom,
1-D quantum harmonic oscillator.
Sturm-Liouville systems. Self-adjoint operators.
Eigenfunctions and eigenvalues.
Hilbert spaces.
Sturm-Liouville system solutions in the orthogonal polynomial class.
Integral transforms (Fourier transform and Laplace transform).
Diffusion equation; simple examples of solution using the separation of variables and Laplace transform techniques. Non-homogeneous equation; source term.
Dirac delta; definitions, properties. Heaviside function. Green function in 1-D case

Seminar classes:
-
Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 101 h
Module ECTS credits 4 ECTS
Participation in lectures 28 h
Realization of independently performed tasks 45 h
Participation in seminar classes 14 h
Preparation for classes 10 h
Contact hours 4 h
Additional information
Method of calculating the final grade:

Ocena z wystąpienia seminaryjnego. Aktywność na zajęciach może ją polepszyć o maksymalnie 1 punkt (stopień).

Grade obtained for the seminar presentation. An active participation in the lectures may enhace the grade (by one point at the most).

Prerequisites and additional requirements:

podstawy rachunku różniczkowego i całkowego oraz algebry.
Basic knowledge of calculus and algebra.

Recommended literature and teaching resources:

1. A. Lenda, „Wybrane rozdziały matematycznych metod fizyki”. UWND AGH 2004.
2. A. Lenda, B. Spisak, „Wybrane rozdziały matematycznych metod fizyki–
rozwiązane problemy” UWND AGH 2006.
4. G.B. Arfken, “Mathematical Methods for Physicists”, Academic Press, (1966–1995)
5. D. McQuarrie, ”Matematyka dla przyrodników i inżynierów”, tom1–3, PWN,2005–6
6. Materiały dydaktyczne na stronie wykładowcy: http://www.ftj.agh.edu.pl/~lenda/mmf23.html

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

None