Print

COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 362DIFFERENTIAL GEOMETRY3 + 06th Semester6

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Elective
Course Objective The main objective of this course is to introduce surfaces theory on Euclid space of n-dimension. Also, to provide the student with a clear presentation of the basic concepts and principles of differential geometry.
Course Content Theory of Surfaces, Manifolds, Covarient Derivation, Orientation, Geodesics, Parallelism, Weingarten Transformation, Gauss Transformation, Main Forms, Gauss and Mean Curvature, Asymptotic and Geodesic Curves, Euler Theorem, Olin-Rodrigues Formulas, Gauss Equation, Curvature of n-Dimensional Euclid Surface, Hypersurface Examples, Regle and Parallel Surfaces.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Defines the basic concepts of differential geometry.
2Relates the Mathematics and basic sciences to the field of differential geometry.
3Compares the structure of Euclidean space with the structure of affine space.
4Decides that Euclidean space is a topological structure.
5Solves problems on manifolds.
6Adapts the basic derivative along the vector field and differential manifold concept to the concepts of derivative and differential derivative.
7Teaches the Gradient Divergence and the geometric properties of the rotational functions.
8Explain the concept of the curve, gives the curvatures and their geometric meaning.
9Defines Serret-Frenet vectors and correlates these with the structure of derivatives.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10
LO 001   5      
LO 002  5       
LO 003    5     
LO 004          
LO 005 5        
LO 0064      4  
LO 0074       4 
LO 008    5     
LO 009       44 
Sub Total855510  88 
Contribution1111100110

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Mid-terms15656
Final examination15858
Total Work Load

ECTS Credit of the Course






156

6
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2016-2017 Spring1CANSEL AYCAN
Details 2015-2016 Spring1CANSEL AYCAN
Details 2014-2015 Spring1CANSEL AYCAN
Details 2013-2014 Spring1CANSEL AYCAN
Details 2012-2013 Spring1ŞEVKET CİVELEK


Print

Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 362 DIFFERENTIAL GEOMETRY 3 + 0 1 Turkish 2016-2017 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0311 %70
Goals The main objective of this course is to introduce surfaces theory on Euclid space of n-dimension. Also, to provide the student with a clear presentation of the basic concepts and principles of differential geometry.
Content Theory of Surfaces, Manifolds, Covarient Derivation, Orientation, Geodesics, Parallelism, Weingarten Transformation, Gauss Transformation, Main Forms, Gauss and Mean Curvature, Asymptotic and Geodesic Curves, Euler Theorem, Olin-Rodrigues Formulas, Gauss Equation, Curvature of n-Dimensional Euclid Surface, Hypersurface Examples, Regle and Parallel Surfaces.
Topics
WeeksTopics
1 The theory of curves, change of parameters
2 Serret-Frenet vectors and vector fields
3 Curvature, curvature axes, centers of curvature, curvature spheres
4 Osculating spheres, involute-evolute
5 Riemann manifold, the covariant derivative
6 Normal vector field, orientation, geodesics
7 Parallelism, Figure operator
8 Midterm Exam
9 Gauss transformation, matrix calculation of Weingarten transformation
10 Basic forms, algebraic invariants of Figure operator
11 Principal curvatures, principal directions, mean curvature, curvature lines
12 Euler's theorem and mean curvatures
13 Olin Rodriges formulas, Dupin indicatrix
14 Final Exam
Materials
Materials are not specified.
Resources
ResourcesResources Language
Türkçe
Diferensiyel Geometri I,II (H.H.Hacısalihoğlu)Türkçe
Türkçe
Türkçe
Türkçe
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