COURSE UNIT TITLE

: THEORY OF MANIFOLDS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4029 THEORY OF MANIFOLDS 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

This course aims at introducing students to the notion of differentiable manifolds and basic concepts and tools for their study, such as differential forms, exterior differentiation and integration.
Learning

Learning Outcomes of the Course Unit

1   will be able to give the definition of topological manifold and differentiable manifold
2   will be able to state the inverse function theorem
3   will be able to calculate the rank of a mapping
4   will be able to multiply Tensor fields
5   will be able to calculate the integral of a differential form over manifolds
6   will be able to know the basic ideas of the de Rham theory

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Euclidean space, Topological manifold, manifold examples via cutting and gluing
2 Euclidean space, Topological manifold, manifold examples via cutting and gluing
3 Tangent vectors, Vector fields
4 The inverse function theorem, The rank of a mapping
5 Differentiable manifold, Differentiable functions and mappings, Rank of a mapping and Immersions
6 Submanifolds, Lie groups
7 Transformation groups and covering manifolds
8 Problem Solving session
9 Vector fields on a manifold
10 Tangent covectors, Bilinear forms, Tensor fields
11 Multiplication of tensors, Orientation of manifold and the volume element
12 Integration in Euclidean space, Integration on Lie groups
13 Manifolds with boundary, Integration on a manifold
14 Stokes theorem, some applications of differential forms

Recomended or Required Reading

Textbooks:
1. Boothby, W. M., An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed., Academic press, 2002, ISBN 978-012116051767
Supplementary Books:
2. Tu, L. W., An Introduction to Manifolds, Springer, 2007, ISBN 978-0387480985
3. Spivak, M., Calculus on Manifolds, Westview Press, 1971, ISBN 978-0805390216
4. Munkres, J. R., Analysis on Manifolds, Westview Press, 1997, ISBN 978-02013159

Planned Learning Activities and Teaching Methods

Lectures, Lecture notes and 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


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

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 : 0 232 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 30 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 176

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1534433
LO.25344334
LO.35434343334
LO.454343333
LO.5543433333
LO.655334333332

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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