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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 3042 ADVANCED DIFERENTIAL GEOMETRY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ILHAN KARAKILIÇ

Offered to

Mathematics (Evening) Mathematics

Course Objective

The aim of this course is to define the surfaces, and to learn how to compute lengths, areas, and curvatures on surfaces in Euclidean three space.

Learning Outcomes of the Course Unit

1   The students who succeeded in this course will be able to define the surfaces in 3 dimensional Euclidean space. 2   The students who succeeded in this course will be able to compute lengths, areas, and curvatures on surfaces. 3   The students who succeeded in this course will be able to define the shape of a surface. 4   The students who succeeded in this course will be able to define flat surfaces and minimal surfaces. 5   The students who succeeded in this course will be able to use the idea of shortest paths on a surface.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 The first fundamental form. 2 Isometries of surfaces. 3 Tangent developable surfaces. 4 Conformal mappings of surfaces. 5 Surface area. 6 The second fundamental form. 7 The curvature of curves on surfaces. 8 Problem solving session 9 The normal and the principal curvature. Meusnier's theorem. 10 The geometric interpretation of principal curvatures. 11 The Gaussian and the mean curvatures. 12 Flat surfaces. 13 Geodesics. 14 Minimal surfaces.

Recomended or Required Reading

Textbook(s): B. O'Neill, Elementary Differential Geometry, Academic Press. Supplementary Book(s): A. Pressley, Elementary Differential Geometry, Springer. M. P. 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 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

Midterm, Final

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: ilhan.karakilic@deu.edu.tr Office : (232) 3018589

Office Hours

TBA

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 14 4 56 Preparation for midterm exam 1 30 30 Preparation for final exam 1 35 35 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 181

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 PO.12 PO.13 LO.1 5 5 4 5 5 5 LO.2 5 5 3 5 5 5 LO.3 5 5 4 5 5 5 LO.4 5 5 3 5 5 5 LO.5 5 5 3 5 5 5