# Course syllabus B-MAT3E - Mathematics 3 (FEEIT - WS 2019/2020)

**Information sheet**ECTS Syllabus

Slovak

**English**

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

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

Course unit code: | B-MAT3E | ||||||||||||

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

Mode of delivery, planned learning activities and teaching methods: | |||||||||||||

| |||||||||||||

Credits allocated: | 6 | ||||||||||||

Recommended semester/trimester: | Automotive Mechatronics - bachelor (compulsory), 3. semester Electrical Engineering - bachelor (compulsory), 3. semester Electrical Power Engineering - bachelor (compulsory), 3. semester Nuclear and Physical Engineering - bachelor (compulsory), 3. semester | ||||||||||||

Level of study: | 1. | ||||||||||||

Prerequisites for registration: | passed Mathematics 2 (B-MAT2E) | ||||||||||||

Assesment methods: | |||||||||||||

Three semestral tests (40 minutes) 20 points. For credit sum of two best evaluated tests (40% of total), written exam (120 minutes) 60 points (60% of total). Total evaluation - sum of points from tests and exam using official classification table. | |||||||||||||

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 methods of 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. | |||||||||||||

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: | |||||||||||||

| |||||||||||||

Language of instruction: | slovak or english | ||||||||||||

Notes: | |||||||||||||

Courses evaluation: | |||||||||||||

Assessed students in total: 124
| |||||||||||||

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

Last modification: | 6. 5. 2019 | ||||||||||||

Supervisor: | doc. RNDr. Ľubomír Marko, PhD. and programme supervisor |

*Last modification made by RNDr. Marian Puškár on 05/06/2019.*