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Обычная версия сайта
2020/2021

Научно-исследовательский семинар "Комплексный анализ"

Статус: Дисциплина общефакультетского пула
Когда читается: 3, 4 модуль
Охват аудитории: для своего кампуса
Язык: английский
Кредиты: 6

Course Syllabus

Abstract

The course is aimed to formation of structured analytical thinking of students and their acquaintance with the basic concepts and methods of complex analysis. The course is based on introductory courses of real analysis, geometry, differential equations and smooth manifolds. The knowledge and skills gained in mastering the discipline can be usefull for studying such courses as Hamiltonian mechanics, Field theory, Complex geometry, Riemann surfaces, PDE analysys and many others
Learning Objectives

Learning Objectives

  • The course is aimed to formation of structured analytical thinking of students and their acquaintance with the basic concepts and methods of complex analysis. The course is based on introductory courses of real analysis, geometry, differential equations and smooth manifolds.
Expected Learning Outcomes

Expected Learning Outcomes

  • Formation of structured analytical thinking. Acquaintance with the basic concepts and methods of complex analysis.
Course Contents

Course Contents

  • Complex differentiability
  • Linear fractional transformations
  • Analytical functions
  • Laurent series
  • Isolated singular points
  • Residues
  • Complex integrability
Assessment Elements

Assessment Elements

  • non-blocking Written exam
  • non-blocking Written test
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.6 * Written exam + 0.4 * Written test
Bibliography

Bibliography

Recommended Core Bibliography

  • Basic complex analysis, Marsden, J. E., Hoffman, M. J., 1999
  • Complex analysis : an introduction to the theory of analytic functions of one complex variable, Ahlfors, L. V., 1979
  • Narasimhan, R. (1985). Analysis on Real and Complex Manifolds. Amsterdam: North Holland. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=342519
  • Real and complex analysis, Rudin, W., 1987

Recommended Additional Bibliography

  • Complex analysis, Lang, S., 2003