FAKULTETA ZA GRADBENIŠTVO, PROMETNO INŽENIRSTVO IN ARHITEKTURO


Subject
 MATHEMATICS C - VECTOR CALCULUS 
https://aips.um.si/PredmetiBP5/UcnaEnotaInfo.asp?Zavod=16&Jezik=A&Leto=2017&Nacin=&Predmet=16U051

Study unit code    16U051 2017

Level Study program or it's part Year Semester
1 BU10 CIVIL ENGINEERING 2 Winter

ECTS kredits 5

Hours - Lectures 45
Hours - Tutorial 30
Hours - Individual Student's Work 75

Lecturers
red. prof. dr. MENCINGER MATEJ

Languages - lectures slovene
Languages - tutorial slovene

Prerequisits
Basic knowledge: Mathematics A - Calculus, Mathematics B – Linear Algebra, Physics, Statics  
Content (Syllabus outline)
VECTOR FUNCTIONS: curves in space, derivatives, connections with physics, natural parameter, curvatres, Frenet formulas PARTIAL DERIATIVES AND APPLICATIONS: scalar fields, level curves, directional derivatives, gradient and maximal derivative, extremal problems, Hesse matrix, classification of extrema, extremal values on boundary, Lagrange multipliers, Taylor series in several variables, vector fields, Jacoby matrix, chain rule and applications, divergence, curl INTEGRALS IN SPACE AND APPLICATIONS: curve diferential, length, work, potential, surface diferential, area, flux, cylindric and spherical coordinates, volume integrals, connections between different types of integrals, Green, Gauss and Stokes formulas, applications of those formulas, integral mean values and theoretical results  
Readings
E. Kreyszig, Advanced Engineering Mathematics, J. Wiley and Sons G. Tomšič, Matematika III, Založba FE in FRI I. Vidav, Višja Matematika, DMFA Slovenije J. Lep, Matematika v snopičih, FG UM M. Mencinger, Zbirka rešenih nalog iz matematične analize in algebre, FG UM M. Mencinger, P. Šparl, B. Zalar, Zbirka rešenih nalog iz matematike II, FG UM  
Objectives and competences
To grasp the basic ideas of matematical modeling of engineering problems 
Intended learning outcomes - knowledge and understanding
Understanding applications of derivative and integral in problems which require several independent variables; understand applicative value of mathematics  
Intended learning outcomes - transferable/key skills and other attributes
Knowledge and being able to apply mathematical tools in engineering courses 
Learning and teaching methods
Classical lectures; occasional use of computer tools for animations that illustrate for instance role of parameters in certain mathematical models  

Assessment Weight (%)
The calculus part (written) 50  
The theoretical part of the exam (written or oral) 50  
[EOP]