|
Week
|
Topics
|
Study Metarials
|
|
1
|
Affine space, Affine frame, Affine coordinate system
|
R1-Chapter 1.1
|
|
2
|
Euclidean space, Euclidean frame, Euclidean coordinate system
|
R1-Chapter 1.2
|
|
3
|
Topological manifolds, Differentiable manifold concept
|
R2-Chapter 1.3, 1.4
|
|
4
|
Tangent vectors, Tangent space
|
R1-Chapter 2.2
|
|
5
|
Vector fields, the space of vector fields
|
R1-Chapter 2.3
|
|
6
|
Directional derivative
|
R2-Chapter 1.6
|
|
7
|
Covariant derivative, Integral curve
|
R2-Chapter 1.6
|
|
8
|
Lie operator
|
R1-Chapter 2.6
|
|
9
|
Cotangent vector, Cotangent space, differential operator
|
R1-Chapter 2.7, 2.8
|
|
10
|
Gradient, Divergence and Curl Functions
|
R1-Chapter 2.9
|
|
11
|
The differentiation of transformation
|
R1-Chapter 2.11
|
|
12
|
Introduction to the theory of curves
|
R1-Chapter 3.1, 3.2, 3.3
|
|
13
|
Reparametrization, arc length parameter
|
R1-Chapter 3.4
|
|
14
|
Serret-Frenet vectors, Osculating hyperplanes
|
R2-Chapter 2.3, 2.4
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
Turkish
|
|
Responsible
|
Asst. Prof. Dr. Kahraman Esen ÖZEN
|
|
Instructors
|
-
|
|
Assistants
|
-
|
|
Resources
|
R1. Yüce, S. (2017). Öklid Uzayında Diferansiyel Geometri, 1. Baskı. Pegem Akademi, Ankara
R2. Hacısalihoğlu, H. H. (2000). Diferensiyel Geometri, Cilt I, 4. Baskı. Ankara Üniversitesi Fen Fakültesi Yayınları, Ankara
|
|
Supplementary Book
|
SR1. Özdemir, M. (2020). Diferansiyel Geometri, 1. Basım. Altın Nokta Yayınevi, İzmir
SR2. Şahin, B. (2021). Diferansiyel Geometri, 1. Basım. Palme Yayınevi, İzmir
|
|
Goals
|
To teach the basic concepts and results of classical differential geometry about Affine space and Euclidean space and to provide the background for students who want to be a graduate student in this field
|
|
Content
|
Euclidean space, Tangent vectors, Vector fields, Covariant derivative, Cotangent vector, Curves
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
-
|
|
2
|
Ability of abstract thinking
|
3
|
|
3
|
To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
|
3
|
|
4
|
Associating mathematical achievements with different disciplines and applying them in real life
|
-
|
|
5
|
Ability to work independently in a problem or project that requires knowledge of mathematics
|
-
|
|
6
|
Ability to work harmoniously and effectively in national or international teams and take responsibility
|
-
|
|
7
|
Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
|
2
|
|
8
|
To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
|
-
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
|
-
|
|
11
|
Being able to produce projects and organize events with social responsibility awareness
|
-
|
|
12
|
Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
|
-
|
|
13
|
Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
|
-
|
|
14
|
Being conscious of acting in accordance with social, scientific, cultural and ethical values
|
-
|