Functional Analysis I

General data

Course ID:	1100-2Ind10
Erasmus code / ISCED:	11.102 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Functional Analysis I
Name in Polish:	Analiza funkcjonalna I
Organizational unit:	Faculty of Physics
Course groups:	Physics (2nd cycle); courses from list "Selected Problems of Modern Physics"
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Prerequisites (description):	(in Polish) Zakłada się znajomość materiału wykładanago w kursach Analiza matematyczna IR i IIR oraz Algebra z geometrią.
Mode:	Classroom
Short description:	Elements of the theory of Hilbert spaces and of the theory of distributions.
Full description:	The aim of the course is to provide necessary knowledge concerning the basic mathematical structures needed in studying theoretical physics. Program: - Banach spaces and linear operators on Banach spaces. - L¹(R^N) space, convolution product, Fourier transform on L¹(R^N) and its properties. - Hilbert space and its properties, basic classes of linear operators (isometries, unitaries, self-adjoint operators). - General theory of orthogonal polynomials. - Fourier transform on L²(R^N). - Fourier series as a unitary transform from L²(Z) to L²([-pi, pi]). - Schwartz space S_N (bi-algebra structure, topology), Fourier transform on Schwartz space and its properties. - Distribution (generalized functions) and their properties, basic operations (differentation, convolution product problem). - Tempered distributions, Fourier transform of tempered distribution. - Support of distribution, distributions with compact support. Student's work load: 140 h includes Lectures and classes: 60 h Preparation for lectures: 45 h Preparation for the exam: 35 h Description by Wiesław Pusz, November 2010.
Learning outcomes:	Knowledge: Familiarity with basic theory of distributions and Hilbert spaces. Skills: Use of distributions and Fourier transform in equations of mathematical physics Attitude: Appreciation of the beauty, depth and usefulness of Hilert spaces and distributions especially in the context of applications to physics.
Assessment methods and assessment criteria:	(in Polish) Forma zaliczenia: egzamin pisemny i egzamin ustny
Internships:	(in Polish) nie dotyczy

This course is not currently offered.

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Copyright by University of Warsaw.