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MZM4 - Selected topics in mathematical analysis

Course specification
Course titleSelected topics in mathematical analysis
AcronymMZM4
Study programme
Module
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ESPB5.0Status
    ConditionCredits from courses equivalent to Mathematics I and Mathematics IIОблик условљености
    The goalThe goal of this course is to teach students basic concepts and theoroms from the following areas: Complex functions of complex variables, Calculus of variations, Series Fourier
    The outcomeThis course provides knowledge that can be applied to other natural science and technical-technological courses taught in the department. The course is intended to enable students to successfully apply the acquired mathematical knowledge in solving techical and technological problems.
    Contents
    Contents of lecturesComplex functions of complex variable-definition, complex sequences, limit and conitnuity, derivative and differentiability, Cauchy-Riemann equations, integration, Cauchy’s integral formulas, Taylor's and Loran's sereies, residues and residue theorem. ; Calculus of variations-unconstrained and constarined minimum of functions of several variables, basic problem of the calculus of variations, problems with high order derivatives Series Fourier-ortogonality of trigonometric functions, Dirichle theorem, seriees Fourier of some functions ; ;
    Contents of exercisesSolving examples and tasks that illustrate various concepts presented in the theoretical contens as well as their mutual relations. Moreover, the practical examples give an opportunity to exercise applying acquired theoretical knowledge to problems of natural and technical-technological sciences.
    Literature
    1. D. Zill, P. Shanahan, A first course in complex analysis, Jones and Bartlett Publishers, Inc., London, 2003
    2. B. Brunt, Calculus of variations, Springer, New York, 2004
    3. .
    Number of hours per week during the semester/trimester/year
    LecturesExercisesOTCStudy and ResearchOther classes
    220
    Methods of teachingLectures
    Knowledge score (maximum points 100)
    Pre obligationsPointsFinal examPoints
    Activites during lecturesTest paper
    Practical lessonsOral examination60
    Projects
    Colloquia40
    Seminars