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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 3051 DIFERENTIAL GEOMETRY COMPULSORY 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

Learning Outcomes of the Course Unit

1   The students who succeeded in this course will be able to make fundamental operations of calculus on Euclidean space. 2   The students who succeeded in this course will be able to define tangent vectors, directional derivative, vector fields, 1-forms, differential forms, mappings, derivative maps. 3   The students who succeeded in this course will be able to define curves, the curvature, and the torsion on the 3 dimensional Euclidean space. 4   The students who succeeded in this course will be able to use the Frenet formulas for the unit speed and the arbitrary speed curves. 5   The students who succeeded in this course will be able to define the surfaces in 3 dimensional Euclidean space.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Euclidean space, tangent vectors, directional derivative, vector fields. 2 The curves in 3 dimensional Euclidean space, velocity, acceleration. 3 1-forms, differential forms, differential operator d, wedge product. 4 Mappings, derivative map, the Jacobien matrix. 5 The curves, speed function, arc length, reparametrizations, vector fields on curves. 6 The Frenet formulas for unit speed curves, the curvature and the torsion. 7 Circular, spherical, planar curves. Curvature center and the curvature radius. 8 Summary and Problem solving 9 The arbitrary speed curves. The velocity, the acceleration and their geometric interpretations. 10 The Frenet formulas for arbitrary speed curves. Spherical image curve. 11 The cylindrical helix. The classification of curves by their curvatures and torsions. 12 Calculus on surfaces. The definition of a surface. Patches. 13 Proper patches. Monge patches. The surfaces given by the implicit functions. 14 Cylinders, spheres, and surface of revolutions.

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)

Assoc.Prof.Dr. Ilhan Karakılıç e-mail: ilhan.karakilic@deu.edu.tr Office : (232) 3018589

Office Hours

To be announced.

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 3 5 5 5 4 LO.2 5 5 5 5 4 LO.3 5 5 3 5 5 5 LO.4 5 5 4 5 5 5 LO.5 5 5 3 5 5 5