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Εικόνα επιλογής

Mathematical Methods in Physics

(Φ-511) -  Spyros Sotiriadis

Περιγραφή Μαθήματος

Course objectives:

The course is addressed to postgraduate and advanced undergraduate students. It provides students with the advanced mathematical tools essential for modern theoretical physics. Emphasising both technique and application, it covers methods such as complex analysis, series and integrals, ordinary and partial differential equations, integral transforms, asymptotic analysis, linear and operator algebra, and probability theory. A central goal is to develop the ability to recognise the underlying mathematical structure of a physical problem, enabling students to map it onto known frameworks and apply appropriate solution strategies. By the end of the course, students will have the mathematical maturity and problem-solving skills needed for advanced study and research in theoretical and computational physics.

 

Course details:

Code Φ-511  
Type B  
ECTS 6  
Hours 5  
Semester Fall  
Lecturer  Spyros Sotiriadis  
Schedule Tuesday
Wednesday		 11:00–13:00 Room 3
11:00–13:00 Room 3
Office hours Wednesday  14:00–16:00, office 220

 

Ημερομηνία δημιουργίας

Τρίτη 3 Νοεμβρίου 2020

Σελίδα μαθήματος
  • Περίγραμμα

    Course Objectives/Goals

    By the end of the course, students should be able to:

    • Master key mathematical techniques commonly used in graduate-level physics.

    • Recognise the role of mathematical structures (e.g., operators, series expansions, integral representations) in physical theories.

    • Identify the underlying mathematical structure of a physical problem and map it onto a standard or previously solved problem.

    • Apply advanced methods to solve representative problems in classical mechanics, electrodynamics, quantum mechanics, and statistical physics.

    • Develop the ability to connect abstract mathematical concepts to physical intuition.

    • Build the mathematical maturity necessary for independent research in theoretical and computational physics.

    Course Syllabus

     

    1. Vector Spaces & Operator Algebra (eigenvalue problems, diagonalisation, Hermitian operators, spectral decomposition, applications in quantum mechanics)

    2. Ordinary Differential Equations (focus on autonomous systems, linearisation and stability analysis)

    3. Partial Differential Equations (Sturm–Liouville theory, separation of variables, Fourier series method, applications: wave, diffusion, Schrödinger equations)

    4. Complex Analysis (residue theorem, contour integration, analytic continuation, branch cuts, applications in evaluating integrals and series)

    5. Asymptotic Methods (asymptotic series, stationary phase, steepest descent, Laplace’s method, WKB)

    6. Integral Transforms (Laplace and Fourier transforms, integral representations of functions)

    7. Green’s Functions (definition and construction, boundary value problems, propagators)

    8. Probability Theory (random variables, distributions, characteristic functions, central limit theorem)

     

    Bibliography

    Main Textbook: 

    George B. Arfken, Hans J. Weber, Frank E. Harris
    Mathematical Methods for Physicists, 7th Edition.
    Academic Press, 2012.

    Further references: 

    • K. F. Riley, M. P. Hobson, S. J. Bence
      Mathematical Methods for Physics and Engineering, 3rd Edition.
      Cambridge University Press, 2006.

    • Michael Stone, Paul Goldbart
      Mathematics for Physics: A Guided Tour for Graduate Students.
      Cambridge University Press, 2009.

    • Carl M. Bender, Steven A. Orszag
      Advanced Mathematical Methods for Scientists and Engineers, Reprint Edition.
      Springer, 1999 (originally McGraw–Hill, 1978).