Week 4: convergence ,Cauchy sequence,completeness.
1) Definition of convergence .
2) cauchy sequence .
3) completenes.
4) convergent sequence.
5) closure and close set.
6) complete subspace.
7) continuous mapping.
Course Material
- Week 1: Introduction to Metric Space
- Week 2: Inqeualitiesc in Metric space
- Week 3: open set ,close set,Neighbourhood
- Week 4: convergence ,Cauchy sequence,completeness.
- Week 5: Completeness Proofs
- Week 6: completeness proofs
- Week 7: Vector space and Sub space.
- Week 8: Mid Term
- Week 9: Norm Space,Banach Space.
- Week 10:Finite Dimensional Normed space and Subspace.
- Week 11: Linear operator
- Week 12:Bounded and Continuous Linear operator.
- Week 13: Linear Functionals And Normed Space of operator.Dual space.
- Week 14:Inner Product Space And Hilbert Space
- Week 15: GramSchmidth Process
- Week: 16 Orthogonal Complement
- Week 17 Banch Fixed point Theorem:
- Week 18:
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Baqir Hussain
