# Mathematics 2 and Mathematics-Economics 4 Spring 2011

## Mathematical Analysis 2

### NEW: Trial exam with answers is available

The trial exam with answers is available here. Answers to Problems 1 and 2 are in Danish, answers to Problems 3 and 4 are in English.

This page is the point of entry for information on the course Mathematical Analysis 2. The formal regulations can be found here. Note that it is a link to the page in Danish.

Prerequisites for the course are the previous three semesters of the education in either Mathematics or Mathemtics-Economics. In particular the course Mathematical Analysis 1 is essential.

### Textbook

We use the following two texts:

Patrick M. Fitzpatrick, Advanced Calculus, Second Edition. American Mathematical Society 2006. ISBN-10: 0-8218-4791-0.
Arne Jensen, A Short Introduction to Complex Analysis, Aalborg 2011.

The first text is the one used for the course Mathematical Analysis 1. The second text is here, and will also be available in a printed version. They are referred to as [PF] and [AJ], respectively.

A hypertext version of [AJ] is available here.

### Supplements

Supplementary notes and comments can be found here.

### Exam and syllabus

The exam is a four hour written exam. The syllabus and information about the exam are given here.

### Plan

Note: This plan is updated as the course progresses.

Session Date Time Topics
1 03.02 12:30-16:15 Infinite series. Review of convergence and divergence. Sequences and series of functions. See Summary 1.
2 07.02 12:30-16:15 Uniform convergence of sequences of functions. Power series. See Summary 2.
3 10.02 12:45-16:30 Integration theory I. See Summary 3.
4 17.02 12:45-16:30 Integration theory II. See Summary 4.
5 21.02 12:30-16:15 Integration theory III. Differential equations I. See Summary 5.
6 03.03 12:45-16:30 Differential equations II. The existence and uniqueness theorem. See Summary 6.
7 14.03 12:30-16:15 The inverse function theorem I. See Summary 7.
8 17.03 12:30-16:15 The inverse function theorem II. The implicit function theorem I. See Summary 8.
9 21.03 12:30-16:15 The implicit function theorem II. See Summary 9.
10 24.03 12:45-16:30 Holomorphic functions and the Cauchy-Riemann equations. See Summary 10.
11 28.03 12:30-16:15 Complex power series. Analytic functions and holomorphic functions. See Summary 11.
12 31.03 12:30-16:15 Contour integrals in the complex plane. See Summary 12.
13 04.04 12:30-16:15 Cauchy's theorems I. See Summary 13.
14 07.04 12:30-16:15 Cauchy's theorems II. Applications of the Cauchy integral formula. See Summary 14.
15 11.04 12:30-16:15 Meromorphic functions. See Summary 15.
16 12.04 12:30-16:15 The residue theorem. See Summary 16.
17 14.04 12:30-16:15 Review and Exercises. See Summary 17.
18 18.04 12:30-16:15 Applications of the residue theorem. See Summary 18.
19 19.04 12:30-16:15 Exam problems. See Summary 19.
20 28.04 12:30-16:15 Overview of the course. About the exam. See Summary 20.

### Exam problems

A collection of exam problems from previous years is available here.
Website maintained by Arne Jensen, matarne at math.aau.dk
Updated 31/05/2011 13:30