Functional Analysis
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WIFA08 
Vaknaam  Functional Analysis 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Functional Analysis  
Leerdoelen  1. The student can prove that a given linear space is a Banach space or a Hilbert space. The student can connect the material of this course with topics from the earlier courses Linear Algebra, Analysis, and Metric Spaces. (Ch. 1, 2, 3) 2. The student can calculate the norm, adjoint, inverse, the spectrum, and the resolvent of a concrete linear operator. (Ch. 2, 4, 5, 6) 3. The student can formulate the main theorems treated in the course, such as the HahnBanach theorem, the open mapping theorem, and the uniform boundedness principle. The student is able to apply these theorems in concrete problems. (Ch. 5, 6) 4. The student can 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. (Ch. 7) 5. The student can apply the methods of functional analysis to concrete problems in mathematics, such as 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, norm, compactness, adjoint, and spectrum. Applications to integral and differential equations are discussed. Further topics include Hermitian operators, projections, the HahnBanach theorem, open mapping theorem, the uniform boundedness principle, and weak convergence.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The grade for this course is computed as max(WE, 0.7 WE + 0.3 HW) where WE is the mark for the written (re)exam and HW is the mark for the average of the homework assignments) 

Vaksoort  bachelor  
Coördinator  dr. A.E. Sterk  
Docent(en)  dr. A.E. Sterk  
Verplichte literatuur 


Entreevoorwaarden  This course builds on the courses Linear Algebra 1, Linear Algebra 2, Analysis, Ordinary Differential Equations, and Metric Spaces.  
Opmerkingen  These lecture notes will be made available through the repro service before the start of the course. Exercises and homework assignments can be downloaded from Nestor.  
Opgenomen in 
