Mathematics (English) | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code: | MATH372 | ||||
Course Name: | Differential Geometry | ||||
Semester: | Spring | ||||
Course Credits: |
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Language of instruction: | English | ||||
Course Condition: | |||||
Does the Course Require Work Experience?: | No | ||||
Type of course: | Compulsory Courses | ||||
Course Level: |
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Mode of Delivery: | Face to face | ||||
Course Coordinator: | Prof. Dr. SELÇUK DEMİR | ||||
Course Lecturer(s): | Prof. Dr. Selçuk Demir | ||||
Course Assistants: |
Course Objectives: | The course aims to introduce the concepts of differential geometry and to study the curves and surfaces in 3 dimensional Euclidean space. |
Course Content: | The content of the course consists concepts and methods of differential geometry and some significant results related to curves and surfaces in 3 dimensional eulidean space. |
The students who have succeeded in this course;
1) will be able to do calculus on Euclidean spaces, 2) will be able to understand notions of tangent vector, directional derivative, vector field, differential forms, and geometric transformations. 3) will be able to understand the notions of the curvature and torsion of a curve in 3 dimensional Euclidean space. 4) will be able to know the basic concepts of surfaces and will be able to do calculus on surfaces. |
Week | Subject | Related Preparation |
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 Jacobian 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) | Midterm Exam | |
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. |
Course Notes / Textbooks: | ders notları |
References: | B. O'Neill, Elementary Differential Geometry, Academic Press. |
Course Learning Outcomes | 1 |
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Program Outcomes | |||||||||||
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | |||||||||||
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | |||||||||||
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | |||||||||||
4) Have the ability to think analytically and use the time effectively in the process of deduction. | |||||||||||
5) Have the ability to search the literature, understand and interpret scientific articles. | |||||||||||
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |||||||||||
7) Have the ability to work efficiently in interdisciplinary teams. | |||||||||||
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |||||||||||
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |||||||||||
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | |||||||||||
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. |
No Effect | 1 Lowest | 2 Average | 3 Highest |
Program Outcomes | Level of Contribution | |
1) | Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | |
2) | Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | 2 |
3) | Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | |
4) | Have the ability to think analytically and use the time effectively in the process of deduction. | 3 |
5) | Have the ability to search the literature, understand and interpret scientific articles. | |
6) | Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |
7) | Have the ability to work efficiently in interdisciplinary teams. | |
8) | Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |
9) | Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |
10) | Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | 3 |
11) | Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. | 3 |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 1 | % 40 |
Final | 1 | % 60 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 40 | |
PERCENTAGE OF FINAL WORK | % 60 | |
total | % 100 |
Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
Course Hours | 13 | 0 | 3 | 39 | |||
Application | 13 | 0 | 0 | ||||
Study Hours Out of Class | 13 | 0 | 3 | 39 | |||
Midterms | 1 | 0 | 15 | 15 | |||
Final | 1 | 0 | 25 | 25 | |||
Total Workload | 118 |