MM406E : Functional Analysis

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Elective

Credits

03

Prerequisite

MM304

Overview

This course offers students different metric spaces, standard spaces and Panach spaces as it addresses the variation of Holder menkowski, Reese theory, Fisher, Hannah-Panach theory and the theory of completion. The Rapporteur is also interested in the study of Helbert spaces and interrelated systems, which are presented on linear and limited effects on different spaces.

Intended learning outcomes

With the end of the course, the student must be able to:

1. Recognizes metric spaces, system space and Punch space.

2. It shows linear dalits, linear effects on expired spaces.

3. Helbert Space explains the L_2، and impact of Helbert facilities.

4. It shows a basic demonstration of orderly space, Punch space and Panach's fixed point proof.

5. Discover metric spaces, system space and Punch space.

6. Distinguishes between linear dalits, and linear effects on expired spaces.

7. Helbert space explains the L_2، and influential Helbert facilities.

8. A basic demonstration of orderly space, Punch space and Panach's fixed point demonstration.

9. The student should resolve a number of trainings and issues with more than one idea of metric spaces, system space and Punch space.

10. The student uses linear dalits, and linear effects on expired spaces.

11. Give students solutions to new, different and multiple problems from Helbert's L_2، space and Helbert's utility effect.

12. The student should apply a basic demonstration about regular space, Panakh space and Panakh fixed point proof

Teaching and learning methods

Theoretical lectures

2. Discussion and dialogue

3. Brainstorming

4. Use sports proof methods

5. Exercises, trainings and solving multifaceted issues

Methods of assessments

Written exam (essay + objective) = 25 degrees or leaves its estimate to the course professor

2. Short tests (editorial or oral), proof assignments, applications, exercises and presentation = 15 degrees or leaves their estimate to the rapporteur's professor

3. Editorial final exam (essay + objective) = 60 degrees

Course content:

Exercises	Lab	Lecture	Number of hours	Scientific topic
1	-	2	3	Metric spaces
1	-	2	3	System Space
2	-	4	6	Punch Space
First Half Exam (2 hours) Week 5
2	-	2	4	Linear functions
1	-	2	3	Linear effects on expired spaces
2	-	4	6	Helbert Space Study
Second half-time exam (2 hours) Week 10
2	-	2	4	Helbert Utility Influencer
1	-	2	3	Basic Proof of Orderly Space
1	-	2	3	Basic proof about Punch Space
1	-	2	3	Banach Fixed Point Proof
Final Exam
			42		Total

References:

Reference Address	Publisher	Version	Author
Functional Analysis			Walter Rodin
Input to functional analysis and its applications	First	Tripoli University	Irwin Hrisek Translation by Dr. Khader Hamid Al-Ahmed

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