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22ZP27 - Differential equations

Course specification
Course titleDifferential equations
Acronym22ZP27
Study programmeBiochemical Engineering and Biotechnology,Environmental Engineering,Material Engineering,Metallurgical Enginering
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 theorems from the following areas: ordinary differential equations, systems of ordinary differential equations, partial differential equations, Laplace transformations.
    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, as well as in mathematical processing of experimental data.
    Contents
    Contents of lecturesOrdinary differential equations – the first-order differential equations, differential equations of the second and higher orders, some applications of ordinary differential equations; Systems of ordinary sifferential equations-definition, methods of solution; some applications of systems of ordinary differential equations; Partial differential equations- the first order partial differential equations, the second order partial differential equations, numerical solution of partial differential equations, some applications of partial differential equations; Laplace transformations- definition, properties, inverse Laplace transformations, application of Laplace transformations to solving differential equations and systems of differential equations.
    Contents of exercisesThe aim of the practices is to solve examples and tasks that illustrate various concepts presented in the theoretical lessions as well as their mutual relations. Moreover, the practices give an opportunity to exercise applying acquired theoretical knowledge to problems of natural and technical-technological sciences.
    Literature
    1. N.Miličić, K. Obrenović Gilmor, B. Zlatić, Zbirka zadataka iz diferencijalnih jednačina sa elementima teorije, 386 str., TMF, Beograd, 2012.(Solved problems with elements of theory on differential equations).
    2. F.S. Merrit, Applied Mathematics in Engineering Practice, McGraw-Hill, New York, 1970.
    3. Tom M. Apostol, Calculus, volume II, Blaisdell Publishing Company, 1964.
    4. N.V. Kopchenova and I.A. Maron, Computational mathematics, worked examples and problems with elements of theory, Mir Publishers,1975.
    Number of hours per week during the semester/trimester/year
    LecturesExercisesOTCStudy and ResearchOther classes
    13
    Methods of teachingLectures and practices
    Knowledge score (maximum points 100)
    Pre obligationsPointsFinal examPoints
    Activites during lecturesTest paper
    Practical lessonsOral examination60
    Projects
    Colloquia40
    Seminars