DZM1 - Selected topics in mathematical analysis

Course specification
Course titleSelected topics in mathematical analysis
Study programme
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      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 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 ; Solving 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. ;
      Contents of exercises
      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. K.U.Šahno, Эlementы teorii funkciй kompleksnnoй peremennoй i operacionnogo isčisleniя, Vыšeйšaя škola, Minsk, 1975. ; (Original title)
      Number of hours per week during the semester/trimester/year
      LecturesExercisesOTCStudy and ResearchOther classes
      Methods of teachingLectures
      Knowledge score (maximum points 100)
      Pre obligationsPointsFinal examPoints
      Activites during lecturesTest paper
      Practical lessonsOral examination60