COURSE INFORMATON
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 Type
Course Coordinator Prof.Dr. Ali Arslan ÖZKURT
Instructors
Prof.Dr.DOĞAN DÖNMEZ1. Öğretim Grup:A
Prof.Dr.DOĞAN DÖNMEZ2. Öğretim Grup:A
 
Assistants
Goals
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.
Content
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.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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
TextbookCalculus 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)
Additional Resources