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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6051 INTRINSIC GEOMETRY OF SURFACES ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ILHAN KARAKILIÇ

Offered to

Mathematics (English) Mathematics (English)

Course Objective

The aim of this course is to define the basic definitions of intrinsic geometry of surfaces.

Learning Outcomes of the Course Unit

1   will be able to understand shape operators 2   will be able to understand normal and gaussian curvatures 3   will be able to learn isometries and the local isometries 4   will be able to define the intrinsic geometry of surfaces 5   will be able to define isometric invariants

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Surfaces in Euclidean three space 2 Shape operators 3 Normal and Gaussian curvatures 4 Computational Techniques 5 Special Curves in a Surface 6 The Fundamental Equations 7 Form Computations 8 Midterm 9 Some Global Theorems 10 Isometries and the local isometries 11 Intrinsic Geometry of surfaces in Euclidean three space 12 Isometric invariants 13 Orthogonal Coordinates 14 Integration and Orientation

Recomended or Required Reading

Textbook(s)/References/Materials: Textbook(s): B. O'Neill, Elementary Differential Geometry, Academic Press. Supplementary Book(s): A. Pressley, Elementary Differential Geometry, Springer. M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall.

Planned Learning Activities and Teaching Methods

Lecture notes Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

E-Mail: ilhan.karakilic@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 5 65 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 4 10 40 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 200

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 5 5 5 5 5 5 LO.2 5 5 5 5 5 5 5 5 5 LO.3 5 5 5 5 5 5 5 5 5 LO.4 5 5 5 5 5 5 5 5 5 LO.5 5 5 5 5 5 5 5 5 5