HOMOLOGY,ARGUMENT PRINCIPLE,RESIDUE THEOREM,POISSON FORMULA
Download as PPTX, PDF0 likes15 views
The document provides a complex analysis overview, covering topics such as homology, the residue theorem, the argument principle, Laurent series, and the Poisson formula. Homology is introduced as a method of linking algebraic objects with topological spaces, initially defined in algebraic topology. Laurent series are explained as a technique for expressing complex functions when Taylor series are inapplicable due to non-analytic points.
1 of 10
Download to read offline
More Related Content
Recently uploaded (20)
Ad
Featured (20)
Ad
HOMOLOGY,ARGUMENT PRINCIPLE,RESIDUE THEOREM,POISSON FORMULA
- 1. Complex analysis Presented by M.VIJAYALAKSHMI M.Sc.,M.Ed ASSISTANT PROFESSOR SRI SARADA NKETAN COLLEGE OF SCIENCE FOR WOMEN,KARUR
- 2. CONTENT • HOMOLOGY • RESIDUE THEOREM • ARGUMENT PRINCIPLE • HOMOLOGY • LAURENT SERIES • POISSON FORMULA
- 3. HOMOLOGY • homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology.
- 10. LAURENT SERIES • Laurent's Series is used to express the complex function when the Taylor series cannot be applied. Laurent's series can be used if a function f(z) is not analytic at a point, but the function is analytic around neighbourhood.