SYLLABUS

University: Technical University of Košice

Faculty: Faculty of Electrical Engineering and Informatics

Department: Department of Physics

Course Number: 26000726

Course Name: Mathematical methods for engineers

Type, scope and method of learning activities: Course Type: Lecture, Numerical exercises Recommended scope of the course content (in hours): Full-time study (hours per week): 2,3 Part-time study (hours per semester): WT 26,39 Study Method: Attendance

Number of credits: 6

Recommended semester of study: WT

Recommended semester

Study programme

Study grade

Study Method

2.rok WT

Physical Engineering of Advanced Materials (FIPM_Bc_D_sk)

Bachelor

Attendance

Level of study:

Prerequisites:

Course completion requirements: Assessment and completion of the course: Credit test and examination Continuous assessment: Student passes the continuous assessment and receives credits when he or she meets the requirement to obtain at least 21% out of 40%. For granting the credit it is necessary to successfully pass two tests of the tasks solved during the semester. Final assessment: Student passes the final assessment and passes the examination when he or she meets the requirement to obtain at least 31% out of 60%. exam Overall assessment: Overall assessment is the sum of the assessments obtained by students in the assessment period. The overall result is determined in accordance with the internal regulations of the Technical University in Košice. (Study Regulations, the internal regulation principles of doctoral studies)

Learning outcomes: Introductory lecture on mathematical methods actively used by physicists and in technology. Instead of formal proofs, the emphasis is put on specific tasks of practical importance, qualitative analysis and methods of simplification for solving the problems on the basis of the physical nature of the investigated processes.

Brief course content: Estimates of mathematical expressions, derivations, integrals and solutions of differential equations. Numerical integration, estimation of sums and series using integration. Mathematical processing of experimental results and the search for empirical formulas. Asymptotes of improper integrals, integration of rapidly changing functions. Stirling formula. The calculations of the sums of numerical and functional series. Integrals depending on a parameter. Multi-dimensional spaces. Use of functions of complex variables in physics. Harmonic functions. Integrals of functions of complex variables. Residues. Dirac delta function and its associated functions. Field theory - scalar field and gradient, potential energy and force, potential, velocity field and flux, divergence of the vector field, continuity equation, Gauss theorem, Poisson's and Laplace's equations in applications. Rotation. Vectors and pseudovectors. Fundamentals of variational calculus, functional, problems of finding the extremes, the Euler equation. Fermat's principle in optics, the principle of least action.

Recommended Reference Sources: 1. J. Mathews, R.L. Walker: Mathematical Methods of Physics, Benjamin, Inc., New York e.a., 1971 2. Ja.B. Zel'dovich, A.D. Myshkis: Elements of applied mathematics. 3nd edition, Nauka, Moskva, 1972 3. E. Kreyszig: Advanced Engineering Mathematics. 8th ed. New York, Wiley a Sons, 1999 4. D. Jordan, P. Smith: Mathematical Techniques. An Introduction for the Engineering, Physical,and Matematical Sciences, 3rd Edition, Oxford Univ. Press, 2002 5. G. Arfken, H. Weber, Mathematical Methods for Physicists, Elsevier, Academic Press, NY e.a., 2006

Recommended optional program components:

Languages required for the course completion: Slovak, English

Notes:

Course assessment: Total number of students assessed: 0

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Teacher: prof. RNDr. Vladimír Lisý, DrSc.

Last modified: 31.08.2022

Approved by: person(s) responsible for the study program