KTH    Matematik






SF2713 Foundations of Analysis

This course is about some principles in Mathematical Analysis, that are fundamental in more advanced studies in related fields.
This means that every concept will carefully be defined and every theorem carefully proved.

Aim of the course: The student is supposed to get a deeper understanding of what real mathematics on a more advanced level is all about. He/she should be able to formulate definitions, stating fundamental theorems, as well as proving them. (se list below). Moreover, the student should be able to use techniques developed in the course to solve problems.

Syllabus: Dedekind´s cut, metric and normed spaces, complete metric and normed spaces, continuity, compactness, Banach´s fixed point theorem, derivative, inverse and implicit function theorem, Stone-Weierstrass theorem, differential forms, Stoke´s theorem, Lebesque integrals.

Prerequisites: Analysis corresponding to SF1602 and SF 1603 or SF1600 and SF1601 and preferably also complex analysis, differential equations and transforms corresponding to SF1628 and SF 1629.

Requirements: Written examinations.

Required reading: Rudin, Walter, "Principles of Mathematical analysis"

Plan for the course We will use Walter Rudin´s classical book: "Principles of Mathematical Analysis", even if I will not do everything exactly as he does.
After each lecture, handwritten notes will be handed out.
During the course there will be three written tests that gives bonus for the final exam.

The first is Monday 26 september an includes chapter 1, 2 and 3 in Rudin.
The second on Tuesday November 8 and includes also chapter 4, 5 and 7.
The third on Friday December 9 and includes also chapter 9 and 10.

The exam concists in eight tasks, each of wich gives at most three points.
If you pass test number k you are not supposed to do task number k on the exam.
The grades are as follows
Fx:11p E:12-13p D:14-15p C:16-18p B:19-21p A:22-24p

Lecture Chapter in Rudin.
1, 2, 3 1
4, 5, 6 2
7, 8 3
9, 10, 11 4
12, 13 5
14, 15, 16, 17 7
18, 19, 20 9
21, 22, 23, 24 10
25, 26, 27 11









Avdelning Matematik Sidansvarig: Hans Tranberg
Uppdaterad: 2011-08-30