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Course, academic year 2024/2025
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Hypercomplex Analysis - NMAA039
Title: Hyperkomplexní analýza
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Vladimír Souček, DrSc.
doc. RNDr. Roman Lávička, Ph.D.
Classification: Mathematics > Geometry, Real and Complex Analysis
Interchangeability : NMAG461
Annotation -
Clifford algebras, Dirac equation, properties of solutions of the Dirac equation on Rn. Monogenic functions, Cauchy theorem and Cauchy integral formula. Taylor and Laurent series. Residuum of monogenic functions, residuum theorem. Conformal invariance.
Last update: G_M (11.10.2001)
Literature - Czech

F.Brackx, R.Delanghe, F.Sommen: Clifford analysis, Pitman, 1982

Last update: Zakouřil Pavel, RNDr., Ph.D. (05.08.2002)
Syllabus -

Clifford algebra of a vector space with a scalar product, Spin group, spinor representations, spinor fields, the Dirac operator. Monogenic functions, connection with harmonic functions, Cauchy theorem, Cauchy integral formula and its applications, Morera theorem, Taylor and Laurent series, residue, residue theorem. Conformal maps in Euclidean space, action of conformal transformations on monogenic funcions, conformal invariance.

Last update: T_MUUK (23.05.2003)
 
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