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Department of Mathematicshttps://www.univ-soukahras.dz/en/dept/math |
Module: Normed vector spaces
| Lecturer | Ali REZAIGUIA |
| Information |
Bachelor - Mathematics
Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/4302 Semester : S5 Unit : UEF 5.1 Credit : 5 Coefficient: 3 |
| Content | Chapter 1: Banach Space Norms, equivalent norms, Banach space Properties of the norm, etc. Examples of Banach spaces Normed vector spaces of finite dimension Continuous linear mappings: Definitions, norm of a continuous linear mapping Dual of a normed vector space Chapter 2: Hilbert Space Scalar product, pre-Hilbert space, Hilbert space Properties of the scalar product, Cauchy-Schwarz inequality, parallelogram equality, etc. Orthogonality, projection theorem, Riesz theorem Orthogonal system (Bessel-Parseval inequality), basis Orthonormal systems Fourier series Complete orthonormal systems in concrete spaces |
| Evaluation | Exam: 60% Directed activities: 40% Evaluation method: Mini Exam: 14 points Participation: 4 points Discipline: 2 points |
