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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 335INTRODUCTION TO DIFFERENTIAL GEOMETRY3 + 05th Semester5,5

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Compulsory
Course Objective The goal of this lecture is to introduce curves theory on Euclid space of n-dimension.
Course Content Euclid Space, Tangent Vectors and Spaces, Vector Fields, Lie Operator, Cotangent Vectors and Spaces, 1-Forms, Gradient, Divergens and Rotational Functions, Derivation Transformation, Theory of Curves, Arc Length, Scalar Velocity, Serret-Frenet Vector Fields and Formulas, Involute, Evolute, Bertrand Curves.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Defines the fundemental theorems anddefinitons about the differential geometry.
2Associates the mathematics and basic sciences with differential geometry.
3Compres the Affin and Euclidean Space.
4Decides that Euclidean space is a topological structure.
5Solves the problems about Manifolds.
6Adapts the basic derivative and differential to vector field along the manifols and differential derivative concepts.
7Teaches the geometric properties of the gradient, divergence and rotational functions.
8Explain the concept of the curve, gives the curvatures and their geometric meaning.
9Defnes the Srret-Frenet vectors and associates these with derivative concepts.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10
LO 001   5      
LO 002  5       
LO 003    3     
LO 004          
LO 005 4        
LO 0063      4  
LO 0074       5 
LO 008      5   
LO 009       4  
Sub Total74553 585 
Contribution1011001110

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Mid-terms15151
Final examination15050
Total Work Load

ECTS Credit of the Course






143

5,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2020-2021 Fall1CANSEL AYCAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 335 INTRODUCTION TO DIFFERENTIAL GEOMETRY 3 + 0 1 Turkish 2020-2021 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0311 %70
Goals The goal of this lecture is to introduce curves theory on Euclid space of n-dimension.
Content Euclid Space, Tangent Vectors and Spaces, Vector Fields, Lie Operator, Cotangent Vectors and Spaces, 1-Forms, Gradient, Divergens and Rotational Functions, Derivation Transformation, Theory of Curves, Arc Length, Scalar Velocity, Serret-Frenet Vector Fields and Formulas, Involute, Evolute, Bertrand Curves.
Topics
WeeksTopics
1 Afin Space, Euclid Space
2 Topological Manifolds, Homeomorfism,Hausdorff space.
3 Diffeomorphism, Differentiable Manifolds, Chart, Atlas.
4 Tangent vectors and Tangent Space
5 Vektor Fields and Vector Fields Space
6 Directed Derivation and Covariant Derivation,
7 Integer Curve, Lie Operator
8 Cotangeny Space, 1-form, Differentiable operatör (Gradient Function, Divergens Function, Rotational Function )
9 Transformation, Coordite Functions, Derivative Function
10 Midterm exam
11 Curves Theory,Parameter Transform, Arc Length
12 Serret-Frenet Vectors
13 Oscülator Hyperplanes, Curvatures
14 Weingarten Operatör, Special Curvature
Materials
Materials are not specified.
Resources
ResourcesResources Language
Diferensiyel Geometri, H.H. HacısalihoğluTürkçe
Diferensiyel Geometri, Mustafa ÖzdemirTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes