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OG07DIR2 - Diferencijalni i integralni racun 2

Course specification
Type of study Bachelor academic studies
Study programme
Course title
Acronym Status Semester Number of classes ECTS
OG07DIR2 mandatory 2 3L + 3E 7.0
Lecturers
Lecturer
Lecturer/Associate (practicals)
    Prerequisite Form of prerequisites
    No prerequisite No prerequisite
    Learning objectives
    Preparing students to understand concepts from the curriculum for their application in professional subjects.
    Learning outcomes
    Acquiring basic mathematical knowledge from mathematical analysis, which is necessary for mastering and understanding professional subjects.
    Content
    The concept of a definite integral and its properties. Newton-Leibniz formula. Improper integral. Application of definite integral. Series. Convergence criteria. Series of functions, domain of convergence. Power series, Taylor and Maclaurin series. Fourier series. Functions of several variables, limits and continuity, geometric interpretation of functions of two variables. Partial derivatives, higher-order partial derivatives, total differential and higher-order differentials. Local and constrained extrema. Concept of double integral, properties and calculation. Variable substitution in double integral. Applications of double integrals (calculation of area, volume, mass, coordinates of center of mass, and moment of inertia). Triple integral, calculation, variable substitution, and applications. Differential equations, first-order differential equations. Higher-order differential equations. Linear nth-order differential equations, linear differential equations with constant coefficients.
    Teaching Methods
    lectures and exercises
    Literature
    1. Zoran Mitrović, Matematička analiza 1, ETF, Banja Luka, 2012. (Original title)
    2. Snježana Maksimović, Diferencijalni i integralni račun 1, Arhitektonsko-građevinsko-geodetski fakultet, Univerzitet u Banjoj Luci, Banja Luka, 2022. (Original title)
    3. Ivan Slapničar, Matematika 2, Fakultet elektronike, strojarstva i brodogradnje, Split, 2008. (Original title)
    4. Zoran Mitrović, Snježana Maksimović, Zbirka riješenih ispitnih zadataka iz matematičke analize 1, ETF, Banja Luka, 2014. (Original title)
    Evaluation and grading
    Written exams, oral exams
    Specific remarks
    Before attending the exercises, students are required to attend lectures and study literature to be familiar with the topics that will be covered in the exercises. A student who unjustifiably misses more than 20% of the classes must renew the subject listening in order to be eligible to take the exam.