COURSE UNIT TITLE

: DIFERENTIAL GEOMETRY

DEGREE PROGRAMMES

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 (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (English)
Mathematics (Evening)

Course Objective

This course is an introductory differential geometry course, and it aims to introduce the main concepts of the theory of curves and surfaces in 3-dimensional Euclidean space.

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

50%(Midterm) + 50% (Final)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture notes on the topics to be covered every week, coming to class by solving the given problems, establishing the concepts by discussing the parts you do not understand with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

Asst.Prof.Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Office Tel.: (0232) 3018585
Office: B212, Mathematics Department

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 25 25
Preparation for final exam 1 25 25
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 166

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1535554
LO.255554
LO.3553555
LO.4554555
LO.5553555

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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