DIFFERENTIAL GEOMETRY

Course Code:

MATH 212

Semester:

Spring

Course Type:

Core

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

6

Prerequisite Courses:

CALCULUS III

Course Language:

English

Course Objectives:

To provide information about the local and global structures of curves and surfaces in three dimensions.

Course Content:

Curves in plane and 3-space, the local theory of curves, Serret-Frenet formulas. Closed curves, isoperimetric inequality and four-vertex theorem. Surfaces, first and second fundamental forms. Geometry of Gauss map. Structure equations. Theorema Egregium. Formulation with differential forms. Gauss-Bonnet theorem. Intrinsic and extrinsic geometry of surfaces.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Learns the local behaviour of curves	1	A
2) Learns the local behaviour of surfaces	1	A
3) Learns how to distinguish local and global behaviours of curves	1	A
4) Learns how to distinguish local and global behaviours of surfaces	1	A
5) Learns how to obtain global information about curves	1	A
6) Learns how to obtain global information about surfaces	1	A

Course Flow

Week	Topics	Study Materials
1	Local Curve Theory in 2D	From textbook 2.1-2.3
2	Local Curve Theory in 3D	2.4-2.6
3	Global Theory of Plane Curves	3.1-3.3
4	Global Theory of Plane Curves	3.4-3.6
5	MIDTERM and discussion of solutions
6	Local Surface Theory (First and Second Fundamental Forms)	4.1-4.3, 4.7
7	Local Surface Theory (Parallelism and Curvatures)	4.4-4.6, 4.8,
8	Local Surface Theory ( Fundamental Theorem of Surfaces)	4.10
9	Local Surface Theory ( Theorema Egregium)	4.9
10	MIDTERM and discussion of solutions
11	Global Theory of Space Curves	5.1-5.3
12	Global Theory of Surfaces (Curvature, Orientability)	6.1-6.3
13	Global Theory of Surfaces (Gauss-Bonnet Formula)	6.4-6.6
14	Global Theory of Surfaces (Index of a Vector Field)	6.7

Recommended Sources

Textbook	R.S. Millman, G.D. Parker, Elements of Differential Geometry, Pearson, 1977
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Quizzes	-	-
Assignments	-	-
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)		x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems					x
5	Consciousness of professional ethics and responsibilty			x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest				x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education			x

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms (Including self study)	2	10	20
Quizzes	-	-	-
Assignments	-	-	-
Final examination (Including self study)	1	18	18
Total Work Load			150
Total Work Load / 25 (h)			6
ECTS Credit of the Course			6

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