| Course Description |
|
| Course Name |
: |
Differential Geometry |
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| Course Code |
: |
MT 321 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
3 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
8 |
|
| Name of Lecturer(s) |
: |
Prof.Dr. DOĞAN DÖNMEZ
|
|
| Learning Outcomes of the Course |
: |
Is able to solve the problems about classical Stokes´ theorem.
Is able to explain the concept of differential forms in space and cubical simplexes.
Is able to explain the generalized Stokes´ theorem
Knows the basic theorems about space curves.
Knows the basic theorems about differentiable surfaces.
|
|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
To teach theories and applications about classical and generalized Stokes´ theorems, to give basic knowledge of curves and surfaces theories, to gain the ability of using analytical geometry, vector calculus and linear algebra knowledge, to teach understanding of abstract mathematical concepts and abstract thinking. |
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| Course Contents |
: |
Classical Stokes´ theorem and some applications, diferential forms and pull-back of diferential forms under diferentiable functions, Generalized stokes´ theorem, curves and characterization of curves by curvature and torsion, Diferentiable surfaces and ruled surfaces. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Faculty of Science Classrooms |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
A brief introduction to Green´s theorem, divergence theorem and surface integral |
Reading the relevant parts of the course material |
Lecture and discussion |
|
2 |
Classical Stokes´ theorem |
Reading the relevant parts of the course material |
Lecture and discussion |
|
3 |
Differential forms and exterior derivative of differential forms |
Reading the relevant parts of the course material |
Lecture and discussion |
|
4 |
Pull back of diferential forms under differentiable functions |
Reading the relevant parts of the course material |
Lecture and discussion |
|
5 |
Generalised Stokes´ theorem |
Reading the relevant parts of the course material |
Lecture and discussion |
|
6 |
The theory of curves and reparametrization by arc length |
Reading the relevant parts of the course material |
Lecture and discussion |
|
7 |
Curvature, torsion and Frenet-Serre equations |
Reading the relevant parts of the course material |
Lecture and discussion |
|
8 |
Midterm-exam |
Review of the topics in the lecture notes and source |
Written examination |
|
9 |
Central curves, helices and involutes |
Reading the relevant parts of the course material |
Lecture and discussion |
|
10 |
Isometries and isometry group of space |
Reading the relevant parts of the course material |
Lecture and discussion |
|
11 |
Characterization of a curve by curvature and torsion |
Reading relevant parts of the course materials |
Lecture and discussion |
|
12 |
Characterization of a plane curve by curvature |
Reading the relevant parts of the course material |
Lecture and discussion |
|
13 |
Differentiable surfaces and implict function theorem |
Reading the relevant parts of the course material |
Lecture and discussion |
|
14 |
Ruled surfaces |
Reading the relevant parts of the course material |
Lecture and discussion |
|
15 |
Solving problems |
Solution of problems in course materials |
Lecture and discussion |
|
16/17 |
Final-exam |
Review of the topics in the lecture notes and source |
Written examination |
|
|
|
Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 İleri Analiz, Ahmet tekcan, Dora Basım Yayın
Yüksek Matematik, Cevdet KOÇAK İTÜ Vakfı Yayınları No:31
Lineer Cebir, H. Hilmi Hacısalihoğlu
Calculus and Analytic Geometry, Authors:Shermann K. Stein, Anthony Barcellos.
A Geometric Approach to Diferential Forms, David Bachman
Differential Geometry, Martin M. Lipschitz,
|
| |
| Required Course Material(s) |
http://math.cu.edu.tr/ddonmez/MT321.htm
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|
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
4 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
4 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
5 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
3 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
5 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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