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Mathematical Methods of Physics, 6 credits
Fysikens matematiska metoder, 6 hp
TFYA18
Main field of study
Mathematics Applied Mathematics Applied Physics PhysicsCourse level
Second cycleCourse type
Programme courseExaminer
Iryna YakymenkoDirector of studies or equivalent
Magnus JohanssonEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied Mathematics, Applied Physics, PhysicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Physics and Nanoscience, Master's programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Analysis, Linear algebra, Vector analysis, Complex analysis, Fourier analysis.Intended learning outcomes
The course is aimed at making the students familiar with the basic equations of the mathematical physics and the methods of their solutions. The emphasis will be done on the special functions involved in the solution of these equations. It will be given much attention to the visualization of the solutions for a number of typical physical problems of current interest. To achieve this goal students have to
- model physical systems in mechanics, hydrodynamics, electrodynamics and quantum mechanics by the wave and heat transfer equations, Poisson, Laplace and Schrödinger equations;
- explore the methods of the solutions of these equations in rectangular, cylindrical and spherical coordinates with corresponding boundary and initial conditions;
- know the properties and how to use in practice the Bessel functions, Legendre polynomials, associative Legendre polymomials, Lagerre and Hermitian polynomials;
- analyze and visualize the solutions in terms of special functions;
- get knowledge of the methods of the random processes theory from the description of correlations in mesoscopic systems.
Course content
Basic equations of mathematical physics and methods of their solutions: separation of variables, orthogonal set expansion, Fourier- and Laplace integral transforms, Green's functions. Sturm-Liouville problem. Bessel functions. Fourier-Bessel series. Boundary value problems in potential theory. Legendre and associative Legendre polynomials. Application of Legendre polynomials in potential theory. Spherical harmonics. Temperature and potential problems in spherical symmetry. Schrödinger equation in cylindrical and spherical symmetry. Theory of Brownian motion. Langevin equation. Fokker-Planck equation. Long-lived correlations in mesoscopic systems. Visualization of the solutions of wave and heat transform equations, vibration of a circular membrane, potential problems in cylindrical and spherical symmetry, hydrogen atom and free particle in central force problem, temperature distribution in a cylindrical bar and a sphere.
Teaching and working methods
Seminars including theory and problem solving following a special plan presented at the beginning of the course. Labs including numerical solutions of partial differential equations.
Examination
| TEN1 | A written examination containing theory problems | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Institutionen för fysik, kemi och biologiDirector of Studies or equivalent
Magnus JohanssonExaminer
Iryna YakymenkoCourse website and other links
http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kkEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Course literature
I.I. Yakymenko. Lecture Notes in Mathematical Methods in Physics. I.I. Yakymenko. Set of Problems in Mathematical Methods in Physics.| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | A written examination containing theory problems | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Course literature is preliminary.
I.I. Yakymenko. Lecture Notes in Mathematical Methods in Physics. I.I. Yakymenko. Set of Problems in Mathematical Methods in Physics.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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X
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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