Welcome to the course.

The schedule for the course can be found via the link to

webTimeEdit top of the page.

Material from the last lecture is added to the Lecture notes. The part on dual of C_0(X) is corrected.

Questions to the oral

exam
Extra lecture 23/11, at 13.15 in MVH11

Lecture from 8/11 is moved to 9/11, at 13.15 in MVL15!!!

Examiner and lecturer: Lyudmila Turowska, Department of Mathematical Sciences, room L3025, tel: 7725341, e-mail: turowska ("vid")
chalmers.se

You can consult the following book:

Gerald B. Folland, Real Analysis, Modern techniques and their Applications, Second Edition, John Wiley & Sons, 1999, Chapters 5-7 and parts of Chapter 4 . I will also produce

Lecture Notes.

Functional analysis arose in early 20th century when the need became apparent to study whole classes of functions rather than individual ones. For example, the investigation of differential and integral equations arising in Physics concerns the study of maps from a set of functions into itself. The basic idea of functional analysis is to apply geometric methods to functions and function spaces. A function is considered as a point in a space, and this space will be a vector space usually of infinite dimension. Geometric objects like balls, and also convergence, are introduced in these spaces. Some important results are the Hahn-Banach theorem and Baire's theorem with consequences. Duality, weak convergence and Alaoglu's theorem are presented. The dual space of continuous functions and the Riesz representation theorem are discussed. Also included is a basic spectral theory of bounded linear operators. The course will consist of lectures and exercise sessions. The exercises will be taken from Folland's book and from sheets handed out during the course.

In the following (F) refers to Folland's book and (N) to Lecture Notes.
Examination consists of the hand-in exercises specified above combined with an oral exam at the end of the course.

In

Chalmers Student Portal you can read about when exams are
given and what rules apply on exams at Chalmers.

At the link

Scedule
you can find when exams are given for courses at University of
Gothenburg.

At the exam, you should be able to show valid identification.

Before the exam, it is important that you report that you want to
take the examination. If you study at Chalmers, you will do this
by the

Chalmers Student Portal, and if you study at University of
Gothenburg, so sign up via

GU's
Student Portal.

You can see your results in Ladok by logging on to the Student
portal.

At the annual examination:
When it is practical a separate review is arranged. The date of
the review will be announced here on the course website. Anyone
who can not participate in the review may thereafter retrieve and
review their exam on Mathematical sciences study expedition,
Monday through Friday, from 9:00 to 13:00. Check that you have the
right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill
out.

At re-examination:
Exams are reviewed and picked up at the Mathematical sciences
study expedition, Monday through Friday, from 9:00 to 13:00. Any
complaints about the marking must be submitted in writing at the
office, where there is a form to fill out.