Analysis
Teacher
MR. Sasi Bhusan Padhi
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Course Name : Analysis
Course Objectives
- To get sufficient knowledge about different analytical structures, concepts and Theorems.
- In much of analysis, the emphasis is not on finding explicit solutions to specific problems, but rather on determining which problems can be solved and what general properties solutions may share.
Learning Outcomes
Upon successful completion of this course, students will be able to:
- Understand Linear maps, Normed Linear spaces, Inner product spaces.
- Know about Closed Graph and Open Mapping Theorems, Bounded Inverse Theorem.
Course Syllabus
Module-I: Linear space, Hamel basis, Span of a linear space, Quotient space, Product space.
Project-1: A study on Linearspaces.
Module -II: Linear map, Range space, Zero space, Hyperspace, Linear maps on finite dimensional linear spaces.
Project-2: A study on Linear maps.
Module - III: Compactness, Some fundamental theorems regarding compactness.
Project-3: A study on Compactness.
Module - IV: Normed space, Euclidian norm, Sequence spaces, Lp space, Function spaces, Inner product spaces.
Project-4: A study on Normed spaces.
Module – V : Quotient norm, Riesz Lemma, Some theorems regarding normed spaces.
Module – VI : Continuity of linear maps, Complete space, Some fundamental theorems.
Project-5: A study on Continuous linear maps.
Module – VII : Bounded Linear maps, Some fundamental theorems,
Project-6: A study on Bounded Linear maps.
BOOK PRESCRIBED :
Functional Analysis—B. V. Limayee (New Age— International Limited,
Publishers, Second Edition)
Chapters: 2, 2.1, 2.2, 2.3, 2.4, 2.5, 3.5, 3.6, 3.7, 5, 5.1, 5.2, 5.3, 5.4, 6, 6.1, 6.2, 6.3, 6.6, 6.7, 6.8.
Session Plan
Session 1
Linear space
Session 2
Hamel basis
Session 3
Span of a linear space
Session 4
Quotient space
Session 5
Product space
Session 6&7
Project-1: A study on Linear spaces
Session 8
Linear map
Session 9
Range space
Session 10
Zero space
Session 11
Hyperspace
Session 12
Linear maps on finite dimensional linear spaces
Session 13&14
Project-2: A study on Linear maps
Session 15
Compactness
Session 16
Theorem regarding compactness
Session 17
Theorem regarding compactness
Session 18&19
Project-3: A study on Compactness
Session 20
Normed space
Session 21
Euclidian norm
Session 22
Sequence spaces
Session 23
Lp space
Session 24
Function spaces
Session 25
Inner product spaces
Session 26&27
Project-4: A study on Normed spaces
Session 28
Quotient norm
Session 29
Riesz Lemma
Session 30
Theorems regarding normed spaces
Session 31
Theorems regarding normed spaces
Session 32
Continuity of linear maps
Session 33
Complete space
Session 34
Some fundamental theorems
Session 35&36
Project-5: A study on Continuous linear maps
Session 37
Bounded Linear maps
Session 38
Theorem
Session 39
Theorem
Session 40
Theorem
Session 41&42
Project-6: A study on Bounded Linear maps
Our Main Teachers
MR. Sasi Bhusan Padhi works as an Assistant Professor, Department of Mathematics, Centurion University of Technology and Management. He has received M.Sc degree in Mathematics from Berhampur University in the year 2001 with Gold Medal. He has 17 years of teaching experience in different Graduate and Post Graduate colleges. Now he is doing research in […]