|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Differential Geometry *||MT 321||5||4||4||8|
|Prerequisites and co-requisites|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Prof.Dr. Ali Arslan ÖZKURT|
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.
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.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|1||A brief introduction to Green s theorem, divergence theorem and surface integral||Review of the relevant pages from sources|
|2||Classical Stokes theorem||Review of the relevant pages from sources|
|3||Differential forms and exterior derivative of differential forms||Review of the relevant pages from sources|
|4||Pull back of diferential forms under differentiable functions||Review of the relevant pages from sources|
|5||Generalised Stokes theorem||Review of the relevant pages from sources|
|6||The theory of curves and reparametrization by arc length||Review of the relevant pages from sources|
|7||Curvature, torsion and Frenet-Serre equations||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources|
|9||Central curves, helices and involutes||Review of the relevant pages from sources|
|10||Isometries and isometry group of space||Review of the relevant pages from sources|
|11||Characterization of a curve by curvature and torsion||Review of the relevant pages from sources|
|12||Characterization of a plane curve by curvature||Review of the relevant pages from sources|
|13||Differentiable surfaces and implict function theorem||Review of the relevant pages from sources|
|14||Ruled surfaces||Review of the relevant pages from sources|
|15||Solving problems||Review of the relevant pages from sources|
|16-17||Final exam||Review of the topics discussed in the lecture notes and sources|
|Recommended or Required Reading|
|Textbook||Calculus and Analytic Geometry, Authors:Shermann K. Stein, Anthony Barcellos.|
A Geometric Approach to Diferential Forms, David Bachman
Differential Geometry, Martin M. Lipschitz (Schaum´s outline series)