# Course syllabus B-MAT3 - Mathematics 3 (FEEIT - WS 2019/2020)

**ECTS**Syllabus

Slovak

**English**

University: | Slovak University of Technology in Bratislava | |||||||||

Faculty: | ||||||||||

Course unit title: | Mathematics 3 | |||||||||

Course unit code: | B-MAT3 | |||||||||

Mode of completion and Number of ECTS credits: | Exam (5 credits) | |||||||||

Name of lecturer: | doc. RNDr. Ľubomír Marko, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english doc. RNDr. Oľga Nánásiová, PhD. (examiner, instructor, lecturer) | |||||||||

Learning outcomes of the course unit: | ||||||||||

The aim of the subject is to continue in last part of Calculus 2, namely in curve integrals from scalar and vector field, the use of Green theorem – change curve integral over the closed curve to double integral. The next goal is the knowledge from calculus of complex functions of comples variable. The mathodsof evalution complex integral over the curve. In the subject the student obtains knowledge about basic properties of ordinary differential equations of
second order and the methods od its solutions and about the Laplace transform and its use in solutions of initial value problems and electrical circuits. | ||||||||||

Prerequisites and co-requisites: | passed Mathematics 2 or passed Mathematics 2 or passed Mathematics 2 | |||||||||

Course contents: | ||||||||||

The curve, line integral from scalar and vector field over the curve. Green’ s theorem, integral independent from the curve. The limit, continuity and the derivative of complex function of complex variable. Cauchy-Riemann’ s equations, analytic (holomorphic) and harmonic functions. Integral of a complex function of complex variable. Cauchy integral theorem, Cauchy integral theorem formula. Taylor series. Laurent series. Singular points, residues, Cauchy
residue theorem. Problems leading to ordinary differential equations of second order. Homogeneous linear differential equation of second order. Solution of linear differential equation of second order with constant coefficients. Nonhomogeneous linear differential equation of second order with constant coefficients. Laplace transform, basic properties, inverse Laplace transform. Applications of Laplace transform in solutions of initial value problem for ordinary differential equations and electric circuits. | ||||||||||

Recommended or required reading: | ||||||||||

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Planned learning activities and teaching methods: | 3/2 (hours of lectures per week / hours of exercises per week) | |||||||||

Assesment methods and criteria: | Semestral assesment: tests 40% of total Final assesment: written exam 60% of total Total evaluation - sum of points from tests and exam using official classification rate table. | |||||||||

Language of instruction: | Slovak, English | |||||||||

Work placement(s): | There is no compulsory work placement in the course unit. |

*Last modification made by RNDr. Marian Puškár on 05/07/2019.*