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Course title

Differential equations

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Year of study,

study programme

2,

1-31 03 01-02 Mathematics (Research and Pedagogical Activities)

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Semester of study

3

4

Number of credits

4

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Lecturer

Amelkin Vladimir Vasilievich

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Course Objective

The purpose of studying the discipline is to train specialists possessing the knowledge and skills to effectively use 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 must

   know:

– elementary methods of integration of ordinary differential equations;

– formulation of the Cauchy problem;

– existence and uniqueness theorems;

– basic concepts and theorems of the general theory of partial differential equations of the first order;

     be able to:

 – solve the basic types of ordinary differential equations of the first order;

– to set initial and boundary-value problems, to solve questions of existence and uniqueness of initial tasks;

– to make up the differential equations of the family of isogonal trajectories;

– solve linear homogeneous and inhomogeneous partial differential equations of the first order;

     own:

– the main methods of constructing differential models of real phenomena and processes.

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Prerequisites

Algebra. Mathematical analysis. Geometry.

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Course content

Basic concepts of the theory of ordinary differential equations. The simplest mathematical models. The Cauchy problem and the geometric meaning of an ordinary differential equation of the first order in normal form. Equations that are integrable in quadrics. Integrating factor. The Lipschitz condition. Existence and uniqueness theorems. The durability of solutions. First integrals. Estimate of the divergence of solutions. Continuous dependence of the solutions on the initial data and the parameter. Scalar ordinary differential equations of the 1st order in general form. The problem of trajectories. Scalar ordinary differential equations of higher orders in normal form. Linear homogeneous and inhomogeneous partial differential equations of the first order.

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Recommended Literature

1.Амелькин, В.В. Дифференциальные уравнения:  учеб.пособие / В.В.Амелькин.-Минск: БГУ, 2012.-288с.

2.Амелькин, В.В. Дифференциальные уравнения в приложениях. Изд.3-е / В.В.Амелькин.-М.: Книжный дом «Либроком», 2008,-208 с.

3.Федорюк, М.В. Обыкновенные дифференциальные уравнения: учеб.пособие. Изд.2-е / М.В.Федорюк.-М.: Наука, 1985.-448 с.

4.Филиппов, А.Ф. Введение в теорию дифференциальных уравнений: учебник / А.Ф.Филиппов.-М.: Едиториал УРСС, 2004.-240 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. Exam score consist of the current mark (40%) and the oral exam mark (60%).

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Method of certification

Exam