This is the main webpage for TMA4145, Linear Methods, for autumn 2011. On this page, you will find information about the course. More detailed information about the contents of the course can be found on the course wiki. Questions about the course can be asked on the course forum.

The most basic object of study in mathematics is of a process. Processes take in input and spew out output. Almost everything that one wants to study scientifically can be modelled mathematically by a process. Given a process, there are three types of question that one wants to answer:

1. What I put in X, what did I get out?
2. Where I got out Y, where did I start?
3. How I put in X, I got out Y, how did I get it?

We model processes in mathematics by functions. Thus the study of processes leads one, in mathematics, to the study of functions. In the first two questions, the function is (presumably) known and the questions are about studying it. The last question in the list above is concerned with the question of finding a function. To do this, one must have some idea of the types of function that might fit, how these behave, and how to describe them. This involves studying not just one function but whole families of functions.

One of the simplest such cases is the family of continuous functions on the interval. One can think of these as modelling processes whereby:

1. The input is a parameter between 0 and 1.
2. The output is a (real or complex) number.
3. The output depends continuously on the input.

In this course, we shall develop the tools necessary to study such functions and, more importantly, the space of such functions.

Due to the nature of this course there is no single text which we follow. It is therefore not possible to assign a specific textbook for this course. The following is a list of recommended reference books for this course.

In order of use:

• Introductory Functional Analysis with Applications. Kreyszig, John Wiley & Sons. Selected material from chs 1 and 5 will be available as a handout from the department office (cost: 20Kr).
• Linear Algebra. Friedberg, Insel, and Spence, Pearson (ISBN: 0130084514).
• Linear Algebra by Jim Hefferon.
• A First Course in Linear Algebra by Rob Beezer.
• An introduction to Hilbert Space. Young, Cambridge University Press (ISBN 0-521-33717-8). Chs 1-4, 6

Some comments on the texts and their use:

• These books are recommended as reference books rather than text books. This means that they should be viewed as sources for supplementary material to help you understand the material rather than as the primary source.

• The second two linear algebra books are free (see the respective pages for exact details of their licenses), but the first contains more of the material from this course.

• Although the Hilbert space book is an excellent one, we only use a small amount of it. Most of the material on Hilbert spaces is also contained in the first Linear Algebra book. Therefore, if you expect to use Hilbert spaces beyond this course then I recommend that you obtain the book by Young. If you expect that you will not use Hilbert spaces further, then I recommend that you obtain the book by Friedberg et al..

Main Page

Technology permitting, the lectures will be delivered as PDF presentations. I shall endeavour to make the notes available the day before the lecture so that students can "follow along". Assuming that the technology works, there may be additional notes written during the lectures. These will be posted shortly after the lecture finishes. I shall often prepare a little more than I shall actually give, any extra will be taken up in the next lecture or deferred to the wiki.

The lecture notes will be available from the wiki, specifically the page Lecture Notes 2011.

Main Page

Links to official information about this course:

• Description Norsk English
• Final exam dates (scroll down a long way)
• Time plan.

TMA4145h2011

The referance group for this course consists of:

• Marte Lovise Nilsen, marteln æt stud døt ntnu dåt no (BMAT)
• Kine Hansvold, kineauro æt stud døt ntnu dåt no (MTFYMA)
• André Flakke, flakke æt stud døt ntnu dåt no (BMAT)
• Randi Anette Fikkan, randiane æt stud døt ntnu dåt no (Cybernetics)
• Håkon Bull Hove, hakonbul æt stud døt ntnu dåt no (MTFYMA)

• Course wiki
• Course Forum
• math.SE a question-and-answer site for mathematics of all levels

There will be no problem session (øving) in week 34. The first problem sessions will take place in week 35.

Homeworks are due in on Fridays by 3pm in the boxes in the Nordre Lavblokk, 3rd floor which are marked as for this course. Please list the members of your group on the copy that you hand in.

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You are to do the homeworks in groups of about 4 or 5 students. To register for a group, follow the instructions on the course wiki.

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The homeworks will be posted on the course wiki and announced on the course forum.

TMA4145h2011