Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
6MATH372DIFFERANTIAL GEOMETRY3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course Basically, differential geometry is the study of geometric objects using calculus. This course introduces to student major ideas of differential geometry and its applications. Upon completion of this course students will have knowledge of the geometry of curves and surfaces.
Course Content General concepts of geometry. Coordinates in Euclidean space. Riemannian metric. Pseudo-Euclidean space and Lobachevsky geometry. Flat curves. Space curves. The theory of surfaces in three-dimensional space. The concept of area. Curvature. The second fundamental form. Gaussian curvature. Invariants of a pair of quadratic forms. Euler’s theorem. Complex analysis and geometry. Conformal transformations. Isotermal coordinates. The concept of a manifold. Geodesics.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Oktay Pashaev
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
Spivak, M., “A Comprehensive Introduction to Differential Geometry”, Vol. 1, Brandeis University, 1970
Stoker, J.J., “Differential Geometry”, Wiley, 1969

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 27 27
Exams and Exam Preparations 1 120 120
Total Work Load   Number of ECTS Credits 6 183

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand how calculus, topology and linear algebra contribute to studying geometrical objects
2 To be able to solve typical problems associated with this theory
3 The ability to solve standard problems concerning motion of particles in space
4 To understand the distinction between local and global properties in geometry
5 To be able to calculate the curvature for a given space curve
6 The ability to determine the principal curvatures and principal directions at every point of a given surface
7 To be able to calculate the Gauss curvature and the mean curvature at every point of a given surface
8 The ability to apply the general surface theory to surfaces of revolution and to ruled surfaces


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 General concepts of geometry. Coordinates in Euclidean space. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
2 Riemannian metric. Pseudo-Euclidean space and Lobachevsky geometry. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
3 Flat curves. Space curves. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
4 The theory of surfaces in three-dimensional space. The concept of area. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
5 Curvature. The second fundamental form. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
6 1st Midterm Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
7 Gaussian curvature. Invariants of a pair of quadratic forms. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
8 Euler’s theorem. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
9 Complex analysis and geometry. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
10 Conformal transformations. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
11 Isotermal coordinates. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
12 2nd Midterm Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
13 The concept of a manifold. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
14 Geodesics. Do Carmo, M.P., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, 1976
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3 4 3
C2 4 3 4 3
C3 4 3 4 3
C4 4 3 4 3
C5 4 3 4 3
C6 4 3 4 3
C7 4 3 4 3
C8 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=254281&lang=en