Functional Analysis
Faculteit  Science and Engineering 
Jaar  2021/22 
Vakcode  WBMA03305 
Vaknaam  Functional Analysis 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
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 HahnBanach 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 SturmLiouville boundary value problems and integral equations. 

Omschrijving  This course covers the basic concepts of infinitedimensional 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 selfadjoint operators, projections, the HahnBanach 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 


Entreevoorwaarden  This course assumes knowledge of the following courses: Linear Algebra 1, Linear Algebra 2, Analysis, Metric Spaces.  
Opmerkingen  
Opgenomen in 
