Karabakh University Courses
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[RIM 401] Differential Geometry
Instruction Language
Azerbaijani
Course Description
This course explores the geometry of curves and surfaces in three-dimensional Euclidean space using the tools of differential calculus. The curriculum focuses on the theory of curves, including curvature, torsion, and the Frenet-Serret formulas. Students investigate the properties of surfaces, covering first and second fundamental forms, Gaussian and mean curvatures, and the Theorema Egregium of Gauss. The course emphasizes the concept of geodesics—the shortest paths on curved surfaces—and introduces the basics of differentiable manifolds and tensor calculus. By the end of the semester, students will be capable of analyzing the intrinsic and extrinsic geometry of manifolds, providing the mathematical rigor necessary for advanced research in general relativity, computer-aided geometric design (CAGD), and theoretical physics.
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