11111

COURSE INTRODUCTION AND APPLICATION INFORMATION


umi.fbe.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall/Spring
Prerequisites
None
Course Language
Course Type
Elective
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to learn Linear Algebra.
  • will be able to learn Normed linear spaces.
  • will be able to learn Differential Equations.
  • will be able to learn Difference Equations.
  • will be able to learn the Theory of Integration.
Course Description

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Jordan forms and some special classes of matrices. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
2 Singular value decompositions. Pseudoinverses “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
3 Linear systems of equations. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
4 Normed linear spaces, basic inequalities, inner product spaces, orthogonal systems. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
5 Hilbert Spaces. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
6 Differential Equations “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
7 Systems of first order differential equations. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
8 Difference equations. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
9 Integral. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
10 Laplace transforms. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
11 Mean value theorem. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
12 Fixed point theorem. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
13 The inverse function theorem. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
14 The implicit function theorem. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
15 Review. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
16 Review. “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
Course Notes/Textbooks “Advanced Mathematical Methods”, Adam Ostaszewski, 1990, Cambridge University Press
Suggested Readings/Materials “Fixed Point Theory for Lipschitziantype Mappings with Applications” Ravi P. Agarwal, 2009, Springer. Various research papers from recent studies.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
20
Presentation / Jury
1
15
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
4
65
Weighting of End-of-Semester Activities on the Final Grade
1
35
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
15
4
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
8
Presentation / Jury
1
16
Project
Seminar / Workshop
Oral Exam
Midterms
1
35
Final Exams
1
42
    Total
217

 

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

 

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