COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Advanced Mathematical Analysis
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 505
Fall
3
0
3
7.5
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
Second Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Q&A
Lecturing / Presentation
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives This twotier course provides deep understanding of introductory functional analysis. The objective of this course is to cover fundamental topics of functional analysis such as General results about metric spaces: Cauchy sequences, completeness and completion, Normed and Banach spaces: Elementary properties and results.
Learning Outcomes The students who succeeded in this course;
  • will be able to explain general properties of metric and normed spaces and explain the relationship between them.
  • will be able to show similarities and differences between function, functional and operator.
  • will be able to illustrate concepts such as separability, completeness and completeness of vector spaces.
  • will be able to use convergence, limit and being Cauchy sequence by using functional analysis tools.
  • will be able to do the applications of the properties of linear operators and its important aplications whether they are defined on finite or infinite dimension.
  • will be able to define continuity and boundedness for operators, functions and functionals.
Course Description This course aims to teach basic theory and applications of Functional Analysis
Related Sustainable Development Goals

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Sequences and convergence, infinite series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.1, 9.2
2 Sequences and convergence, infinite series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.3
3 Absolute and conditional convergence, Power series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.4, 9.5
4 Power series, Taylor and Maclaurin series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.5, 9.6
5 Taylor and Maclaurin series, Applications of Taylor and Maclaurin series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.6, 9.7
6 Fourier series Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 9.9
7 Midterm
8 Functions of several variables, Limits and continuity Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 12.1,12.2
9 Limits and continuity, Partial derivatives Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 12.2,12.3
10 Partial derivatives, Higher order derivatives Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 12.3,12.4
11 The Chain rule, Gradients and directional derivatives Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 12.5, 12.7
12 Gradients and directional derivatives, Extreme values Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 12.7, 13.1
13 Extreme values of functions defined on restricted regions Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 13.2
14 Lagrange multipliers Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition, (Pearson, 2018). Section 13.3
15 Semester Review
16 Final Exam
Course Notes/Textbooks

Robert A. Adams, Christopher Essex, "Calculus, A complete course", 9th edition, (Pearson, 2018).  ISBN: 9780134154367.

Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
20
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
2
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
14
3
42
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
4
15
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
30
Final Exams
1
45
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest