CIVIL ENGINEERING
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT4053	Differentiable Manifolds	Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :
Recommended Optional Program Components:	None
Course Objectives:	The differentiable manifolds course aims to give the fundamental knowledge for the studies of graduate students who intends to study at geometry.

Learning Outcomes

The students who have succeeded in this course;
upon succeeding this course
1)be able to test a differentiable structure given on a set
2)be able to give examples of Differentiable structures on a set
3) be able to check differentiablity of a function
4) be able to solve problems involving the derived map of a transformation between two manifolds
5) be able to use the properties of induced topology on a manifold,
6) be able to coordinatize Grassmann manifolds and can evaluate their dimensions,
7) be able to understand the existence problems by using the unity of partition
8)be able to explain the derived function of a function by using the Leibniz rule,
9) be able to explain submanifolds as images under Immersions
10) be able to coordinatize quotient manifolds and calculate their dimensions,
11) be able to construct Klein bottle and Mobius strip as an example of a quotient manifold

Course Content

Differentiable (diff.able) functions, Atlas, diff.able structures on a set, Examples of diff.able structures, diff.able manifolds, diff.able functions, The induced topology on a manifold, diff.able varieties, Grassmann manifolds, Manifold structure on a topological space, properties of the induced topology, Topological restrictions on a manifold, Partitions of unity, Partial differentiation, tangent vectors, The invers function Theorem, Leibniz's rule. İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds. Submersions, The fibres of submersions, Quotient manifolds, Transformation groups, Examples of quotient manifolds.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Preliminaires
2)	Some classical theory of differentiable functions
3)	Atlas, differentiable structures on a set
4)	Examples of differentiable structures on a set
5)	Differentiable manifolds
6)	Differentiable functions
7)	The induced topology on a manifold
8)	Differentiable varieties, Grassmann manifolds
9)	Topological restrictions on a manifold, Partitions of unity
10)	Manifold structure on a topological space, properties of the induced topology
11)	Partial differentiation, tangent vectors, derived linear functions, The invers function Theorem, Leibniz's rule.
12)	İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds.
13)	Submersions, The fibres of submersions, Quotient manifolds
14)	Transformation groups, Examples of quotient manifolds.

Sources

Course Notes / Textbooks:	Differentiable Manifolds an Introduction ,F Brickell, R. S. Clark.
References:	.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 45
Final	1	% 55
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 45
PERCENTAGE OF FINAL WORK		% 55
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	7	2	14
Midterms	2	20	40
Final	1	30	30
Total Workload			126

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
2)	Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3)	Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4)	Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5)	Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics.
6)	Ability to work effectively within and multi-disciplinary teams; individual study skills.
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8)	Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9)	To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10)	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11)	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.