26E083OPM3 - Selected Topics in Mathematics 3 with Applications

Course specification
Course title		Selected Topics in Mathematics 3 with Applications
Acronym		26E083OPM3
Study programme
Module
Type of study
Lecturer (for classes)		professor PhD Siniša Ješić professor PhD Nataša Ćirović
Lecturer/Associate (for practice)		professor PhD Nataša Ćirović professor PhD Siniša Ješić
Lecturer/Associate (for OTC)		professor PhD Nataša Ćirović
ESPB		3.0	Status	elective
Condition
The goal		Familiarizing students with the concepts of mathematical analysis in n-dimensional real space and methods to determine extreme values of multivariable real functions, convex sets and multivariable convex functions, with the goal to be able to solve problems of applied mathematics in various areas of Electrical and Computer Engineering.
The outcome		The student is competent to determine extreme values of multivariable real functions and multivariable convex functions and to apply these techniques to solve problems in various fields of Electrical and Computer Engineering.
Contents
Contents of lectures		Multivariable functions: differentiability, differential operators, extreme values, Taylor’s formula, unconditional and conditional extreme values, Lagrange multipliers, Karush-Kuhn-Tucker theorem, convex sets, multivatiable convex functions, first and second order convexity conditions.
Contents of exercises		Through examples and problems, students learn how to apply the theorems and concepts learned in theory, and to solve specific problems using mathematical software such as Matlab and Python with libraries. Students are prepared to solve optimisation problems in Electrical and Computer Engineering.
Literature
Siniša Ješić: Script in Mathematics 3, Multivariable functions, Theory of integrals, Belgrade 2007, in serbian Siniša Vrećica, Convex analysis, second edition, Universitz of Belgrade, Faculty of Mathematics, 1999, in serbian Boyd, S.,Vandenberghe, L. Convex optimization. Cambridge university press, 2004 (Original title)
Number of hours per week during the semester/trimester/year
Lectures	Exercises	OTC	Study and Research	Other classes
1	1	0.5
Methods of teaching		Lectures, exercises, discussions, help with homework using mathematical software such as Matlab and Python with libraries
Knowledge score (maximum points 100)
Pre obligations		Points	Final exam	Points
Activites during lectures		0	Test paper	50
Practical lessons		30	Oral examination	20
Projects
Colloquia		0
Seminars		0