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Methods of integral equations

ДВС.1.03

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

3

LO 2. To have basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, theory of differential equations, in particular partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. LO 7. Be able to conduct practical research and find solutions to incorrect problems. PLO 22.1. Know the main sections of the theory of calculations, theory of algorithms and theory of programming, mathematical logic, theory of probability and mathematical statistics, control theory.

Full-time form

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

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 Terms of semester and final evaluation: 1) control paper I – the first half of the semester 2) control paper 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 The rearrangement of modular control works is not provided for. In case of violation by students during semester evaluation principles of academic integrity, a grade of -5 points is given for the corresponding work.

Ukrainian