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Methods of integral equations

ДВС.1.03

Вибіркова дисципліна для ОП

First

2018/2019

7 Semester

3

PLO1. Demonstrate knowledge and understanding of basic concepts, principles, theories of fundamental and applied mathematics and use them in practice. PLO2. To have basic principles and methods of mathematical, complex and functional analysis... PLO15. Demonstrate the ability to self-study and continue professional development. PLO17. Demonstrate the skills of interaction with other people, the ability to work in teams. PLO19. Communicate effectively about information, ideas, problems and solutions with specialists and society in general. PLO21. Demonstrate professional communication skills, including oral and written communication in Ukrainian and at least one other common European language.

1) Know the main sections of mathematical analysis, algebra and geometry and differential equations 2) To be able to solve problems within the courses "Mathematical analysis 1", "Mathematical analysis 2", "Algebra and geometry", "Differential equations".

Introduction 1 Functional equations and methods of their solution. 2 The simplest integral equations. Reduction to differential equations. 3 Classification of integral equations. Integral equations of Fredholm 4 The method of successive approximations for Fredholm's integral equation 5 Method of iterated kernels for Fredholm's integral equation 6 The Fredholm equation with a degenerate kernel 7 Eigennumbers and eigenfunctions of Fredholm's integral equation Integral equations of Voltaire 8 Method of successive approximations for Voltaire's integral equation 9 Solving Voltaire's integral equation by reduction to a differential equation. 10 Voltaire's equation with a degenerate kernel. 11 Voltaire's equation with a difference kernel. 12 Integra-differential equations.

1. Mikhlin S.G. Lektsii po lineinym integral-nym uravneniiam. M., 1959. — 234s. 2. Chornoіvan Iu. O. Konspekt lektsіi z distsiplіni "Іntegral-nі rіvniannia ta elementi funktsіonal-nogo analіzu" dlia studentіv spetsіal-nostі "mekhanіka" K: 2017. – 203s. 3. P.P. Zabreiko, Koshelev A.I., Krasnosel-skii M.A. i dr. Integral-nye uravneniia. SMB. – M., 1968. – 448 s. 4. M.L.Krasnov, A.I. Kisepev, G.I. Makarenko Integral-nye uravnenie. – M., 2003 – 192s. 5. T.V. Eliseeva. Integral-nye uravneniia i variatsionnoe ischislenie. – Penza, 2008 –104s. 6. Berezanskii Iu.M., G.F.Us, Sheftel- Z.G. Funktsional-nyi analiz. - K.: Vishcha shkola, 1990. - 600s. 7. Liashko S.I., Nomirovskii D.A., Petunin Iu.I., Semenov V.V. Dvadtsataia problema Gil-berta. Obobshchennye resheniia operatornykh uravnenii. M.: OOO “I.D. Vil-iams”, 2009. – 192s ..

Lectures, consultations, independent work

Student evaluation forms: Semester assessment: 1) control paper I – 40 points 2) control work II – 40 points 3) combined assessment for homework - 20 points 4) additional points - up to 15 points Evaluation organization: Terms of semester and final evaluation: 1) control paper I – the first half of the semester 2) control work II - second half of the semester 3) summary assessment for homework - at the end of the semester 4) additional points - at the end of the semester

Ukrainian