MATH371 DIFFERENTIAL GEOMETRY
| Course Code: | 2360371 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 9.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of the course the student will learn
-The basic notions about differential geometry of curves, local information like torsion, curvature and their computations;
-Fundamental Theorem of Local Theory of curves and surfaces;
-The basic notions about differential geometry of regular surfaces, tangent plane, differentiability of maps between surfaces, the notion of differential, orientability, metric properties, the first fundamental form;
-the notion of Gauss map and its fundamental properties and the second fundamental form, the role of these in deriving local properties of the surface; Gaussian and mean curvatures, principal curvatures and directions, their computation;
-the role of first fundamental form understanding the intrinsic properties of surfaces; the notion of covariant derivative of a vector field on a surface; parallel transport and geodesics, the statement of Gauss-Bonnet Theorem.
Course Content
Curves in R3: Frenet formulas and Fundamental Theorem. Regular surfaces. Inverse image of regular values. Differentiable functions on surfaces. Tangent plane; the differential of a map, vector fields, the first fundamental form. Gauss map, second fundamental form, normal, principal curvatures, principal and asymptotic directions. Gauss map in local coordinates. Covariant derivative, geodesics.
Course Learning Outcomes
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution