Mathematical Methods in Physics Field of study: Physics
Programme code: W4-S2FZA22.2025

Module name: Mathematical Methods in Physics
Module code: W4-FZ-NM-S2-1-22-15
Programme code: W4-S2FZA22.2025
Semester: winter semester 2025/2026
Language of instruction: English
Form of verification: exam
ECTS credits: 4
Purpose and description of the content of education:
The lecture includes a coherent and uniform presentation of elements of the theory with justifications and many examples derived from physics and engineering within the following topics: 1. Elements of distribution theory: basic concepts, differentiation of distribution, the Dirac delta, and related distributions, the principal value of the integral; operations on distributions; Sochocki formulas, the convolution of distributions and their Fourier transform. 2. Green's functions of differential operators: boundary issues, related to eigenvalue problem; examples coming from physics and engineering (e.g. Sturm Liouville systems). 3. Elements of Hilbert space theory: basic concepts and examples; orthonormal and Schauder bases; unitary and self-adjoint operators; spectra and eigenvalues; subtleties of the formalism of quantum theory. 4. Fourier series and their properties. 5. Integral transforms; Fourier and Laplace transform and their properties. 6. Elements of signal analysis. The classes and seminars are devoted to solving selected examples and explaining theories in specific physical situations. Students participate in deriving and discussing some formulas and examples from lectures, as well as the discussions of the significance of the discussed formalisms in various physical problems. As part of the student's work the student: 1. strives to consolidate acquired knowledge based on lecture notes and supplementary literature; 2. improves the mathematical skills necessary to solve physical problems; 3. tries to accomplish the tasks proposed by the lecturer. The exam is compulsory.
List of modules that must be completed before starting this module (if necessary): not applicable
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
understanding the civilization meaning of differential and integral calculus and its role in physics [E1]
 KF_W01 [4/5] KF_U01 [4/5]
acquiring a good theoretical and practical intuition related to mathematical analysis; is able to perform basic calculations [E2]
 KF_W02 [4/5] KF_U02 [4/5]
understanding the meaning and can give examples of the physical application of differential equations in physics and technology [E3]
 KF_U01 [3/5] KF_U02 [3/5]
ability to perform simple calculations in Hilbert spaces [E4]
 KF_W05 [3/5] KF_U03 [3/5]
understanding the need to use the distribution theory tools in various branches of physics and engineering [E5]
 KF_W05 [3/5] KF_U03 [3/5]
understanding the ideas underlying Fourier analysis and its applications in various fields of physics and engineering [E6]
 KF_W05 [3/5] KF_U03 [3/5]
awareness of the need to develop mathematical formalism in order to better describe and understand the physical world [E7]
 KF_W01 [4/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [FZ1] 30 Formal lecture/ course-related lecture [a01]  exam E1 E3
discussion classes [FZ2] 30 Explanation/clarification [a05] 
Activating methods: a case study [b07]  		course work E2 E4 E5 E6 E7
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Literature reading / analysis of source materials [a02] Preparation for classes
reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class
Developing practical skills [a03] Preparation for classes
activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)
Getting acquainted with the syllabus content [b01] Consulting the curriculum and the organization of classes
reading through the syllabus and getting acquainted with its content
Studying the literature used in and the materials produced in class [c02] Preparation for verification of learning outcomes
exploring the studied content, inquiring, considering, assimilating, interpreting it, or organizing knowledge obtained from the literature, documentation, instructions, scenarios, etc., used in class as well as from the notes or other materials/artifacts made in class
Implementation of an individual or group assignment necessary for course/phase/examination completion [c03] Preparation for verification of learning outcomes
a set of activities aimed at performing an assigned task, to be executed out of class, as an obligatory phase/element of the verification of the learning outcomes assigned to the course
Analysis of the corrective feedback provided by the academic teacher on the results of the verification of learning outcomes [d01] Consulting the results of the verification of learning outcomes
reading through the academic teacher’s comments, assessments and opinions on the implementation of the task aimed at checking the level of the achieved learning outcomes
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)