Prerequisits
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Basic knowledge:
Mathematics A - Calculus, Mathematics B – Linear Algebra, Physics, Statics
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Content (Syllabus outline)
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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
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Readings
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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
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Objectives and competences
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To grasp the basic ideas of matematical modeling of engineering problems |
Intended learning outcomes - knowledge and understanding
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Understanding applications of derivative and integral in problems which require several independent variables; understand applicative value of mathematics
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Intended learning outcomes - transferable/key skills and other attributes
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Knowledge and being able to apply mathematical tools in engineering courses |
Learning and teaching methods
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Classical lectures; occasional use of computer tools for animations that illustrate for instance role of parameters in certain mathematical models |