Karabakh University Courses
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[RIM 404] Functional Analysis
Instruction Language
Azerbaijani
Course Description
This course explores the generalization of linear algebra and calculus to infinite-dimensional vector spaces. The curriculum focuses on the study of normed linear spaces, Banach spaces, and Hilbert spaces. Students investigate fundamental principles such as the Hahn-Banach theorem, the Open Mapping theorem, and the Closed Graph theorem. The course emphasizes operator theory, covering linear functionals, dual spaces, and the spectral theory of bounded and compact operators. By the end of the semester, students will be capable of applying these abstract frameworks to solve integral equations, understand the foundations of quantum mechanics, and analyze approximation methods in numerical analysis, providing the ultimate theoretical depth required for advanced research in mathematical physics and modern engineering.
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