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Course title |
Differential equations |
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Year of study, study programme |
2, 1-31 03 08 Mathematics and Information Technologies |
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Semester of study |
3 |
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Number of credits |
2 |
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5 |
Lecturer |
Roudenok Alexander Evgenievich |
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Course Objective |
The purpose of studying the discipline is to train specialists possessing the knowledge and skills to use effectively the basic methods of the theory of differential equations to study the phenomena and processes of reality surrounding us. Studying the discipline solves the following tasks: – acquisition by students of knowledge in the field of the theory of differential equations; – acquisition of practical skills in solving mathematical problems, constructing and analyzing mathematical models described by differential equations. As a result of the training, the student should know: – elementary methods of integration of ordinary differential equations; – formulation of the Cauchy problem; – existence and uniqueness theorems; – basic concepts and theorems of the theory of ordinary differential equations; be able to: – Draw up the differential equations of the family of curves; – solve basic types of ordinary differential equations of the first and higher orders; – set the Cauchy problem and solve it, including the methods of successive approximations; own: – the basic methods of constructing differential models of real-life phenomena and processes, methods of solving basic types of ordinary differential equations. |
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Prerequisites |
Algebra. Mathematical analysis. Geometry. |
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Course content |
Differential equations of the first order, solved with respect to the derivative. The simplest mathematical models. The Cauchy problem and the geometric meaning of an ordinary differential equation of the first order in normal form. The main types of differential equations of the first order integrable in quadratures. Integrating factor. Differential equations not solved with respect to the derivative. Picard’s theorem of existence and uniqueness of the solution of the Cauchy problem of first-order DM. Differential equations of higher orders. Methods of lowering the order. Systems of first-order differential equations. The first integral of a system of first-order differential equations. Picard’s theorem of the existence and uniqueness of the solution of the Cauchy problem for a system of first-order differential equations and a n-order differential equation. |
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Recommended Literature |
1.Филиппов, А.Ф. Введение в теорию дифференциальных уравнений: учебник / А.Ф.Филиппов.-М.: Едиториал УРСС, 2004.-240 с. 2.Амелькин, В.В. Дифференциальные уравнения: учеб.пособие / В.В.Амелькин.-Минск: БГУ, 2012.-288с. 3.Федорюк, М.В. Обыкновенные дифференциальные уравнения: учеб.пособие. Изд.2-е / М.В.Федорюк.-М.: Наука, 1985.-448 с. |
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Teaching Methods |
Explanatory-illustrative, reproductive, partially-search |
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Teaching language |
Russian |
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Requirements, current control |
Test papers. Tests. |
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Method of certification |
Credit |