Infopaket

Advanced Topics in Mathematical Analysis

ДВВ.01.02

Обов’язкова дисципліна для ОП

Second

2023/2024

3 Semester

2

PLO4. Be able to determine the type of data integration required for a task. PLO8. Communicate effectively on information, ideas, problems and solutions with professionals and society at large.

Understand the main topics of mathematical analysis, algebra, differential equations, equations of mathematical physics, and functional analysis. Be able to solve standard problems in the aforementioned areas of mathematics.

The course introduces students to the theory of generalized solutions of operator equations, specifically the simplest schemes of generalized solutions of linear operator equations, a priori estimates for a linear continuous operator, the application of the theory to problems in mathematical physics, and the general scheme of generalized solutions of linear and nonlinear operator equations.

1. D.A. Klyushin, S.I. Lyashko, D.A. Nomirovskii, Yu.I. Petunin, V.V .Semenov Generalized solutions of operator equations and extreme elements. Springer, 2012. – 202p. 2. Tymchyshyn I.B., Nomirovskii D.A. Generalized Solvability of a Parabolic Model Describing Transfer Processes in Domains with Thin Inclusions // Differential Equations. – 2021, 57(8). – P. 1053–1062. 3. Kolmogorov A.M., Fomin S.V. Elementy teoriyi funktsiy ta funktsional'noho analizu. — Kyiv: Vyshcha shkola, 1974. — 456 p. 4. Gelbaum Bernard R., Olmsted John M. H. Counterexamples in Analysis. – Courier Corporation, 2003. – 195 p. 5. Rajwade A. R., Bhandari A. K. Surprises and Counterexamples in Real Function Theory. – HINDUSTAN, 2007. – 301 p. 6. Wise Gary L., Hall Eric B. Counterexamples in Probability and Real Analysis. – Oxford University Press, 1993. – 224 p. 7. Schilling René L., Kühn Franziska Counterexamples in Measure and Integration. – Cambridge University Press, 2021. – 431 p.

lectures, academic consultations, tests, quizzes, exams, and homework

Semester assessment: 1. Test – 30 points 2. Combined grade for practical classes – 30 points 3. Additional points – up to 10 points Final assessment in the form of an exam: – 40 points Conditions for students' admission to the final exam: no less than 36 points for the semester assessment. Conditions for receiving a general positive grade for the course: no less than 24 points in the final exam.

Ukrainian