Functional Analysis

Uitgebreide vaknaam	Functional Analysis
Leerdoelen	At the end of the course, the student is able to: 1. prove that a given linear space is a Banach space or a Hilbert space. 2. calculate the norm, adjoint, inverse, the spectrum, and the resolvent of a concrete linear operator. 3. formulate the main theorems treated in the course, such as the Hahn-Banach theorem, Baire's theorem, Zabreiko's lemma, the open mapping theorem, the closed graph theorem, and the uniform boundedness principle. The student is able to apply these theorems in concrete problems and derive simple corollaries from them. 4. give examples of dual spaces and (non-)reflexive spaces. The student can determine of a given sequence whether it converges in the strong, weak, or weak* sense. 5. apply the methods of functional analysis to concrete problems in mathematics, such as Sturm-Liouville boundary value problems and integral equations.
Omschrijving	This course covers the basic concepts of infinite-dimensional linear spaces and the linear maps between them. In particular, the theory of Banach and Hilbert spaces and the operators on them are discussed. Functional analysis is a basic theory for many areas of physics and mathematics (quantum mechanics, partial differential equations, numerical solution methods, etc.). Within this framework attention will be paid to the theory of function spaces. Basic definitions and applications of operators will be discussed: continuity, boundedness, norms, compactness, adjoint, and spectrum. Applications to integral and differential equations are discussed. Further topics include self-adjoint operators, projections, the Hahn-Banach theorem, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and weak convergence.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Werkcollege (T)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE) (Final Grade = max(WE, 0.3 HW + 0.7 WE) only if WE >=4.5, otherwise Final Grade = WE, where HW average homework assignments grade and WE grade final written exam. The same formula applies to the resit exam.)
Vaksoort	bachelor
Coördinator	Prof. Dr. J.G. Peypouquet
Docent(en)	Prof. Dr. J.G. Peypouquet
Verplichte literatuur	Titel Auteur ISBN Prijs “Functional Analysis, an Introduction” Henk de Snoo & Alef Sterk €  10,00 Exercises and homework assignments can be downloaded from Nestor J.G. Peypouquet
Entreevoorwaarden	This course assumes knowledge of the following courses: Linear Algebra 1, Linear Algebra 2, Analysis, Metric Spaces.
Opmerkingen
Opgenomen in	Opleiding Jaar Periode Type BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II a BSc Mathematics and Physics (double degree) 2 semester II a verplicht BSc Mathematics: General Mathematics  ( Major track General Mathematics) 2 semester II a verplicht BSc Mathematics: Probability and Statistics 2 semester II a verplicht BSc Technische Wiskunde 2 semester II a verplicht