Course syllabus

# Introduktion till reell analys

Introduction to Real Analysis

## FMAA60, 7,5 credits, G1 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Introduction to Real Analysis

Valid for: 2018/19

Decided by: PLED F/Pi

Date of Decision: 2018-03-23

Elective for: C1, D1, F1, I1, M1, MD1, N1, Pi1, W1

Language of instruction: The course will be given in Swedish

To supplement the course in single variable calculus with theory
for which there is no room within standard course. The course is
meant for beginning students who already mastered large parts of
the standard course.

Apart from some fixed point theorem no new methods for calculations
are obtained, but many of the methods and more abstract points of
view that are introduced to carry out proofs that are left out of
the standard calculus course make it easier to see patterns and
analogies in later courses.

The new ways of thinking and the concepts give the student a better
capability to creatively attack new problems.

Knowledge and understanding

For a passing grade the student must

- be able to explain why the real numbers are needed in single variable calculus
- be able account for and illustrate concepts that are introduced during the course
- be able to account for the content of definitions, theorems and proofs.

Competences and skills

For a passing grade the student must

- be able to use concepts and methods from the course to carry out comparatively simple proofs.

- The real numbers.
- Topology and compactness.
- More about continuity
- More about derivative
- About integration
- Elementary functions
- Inequalities
- Iteration and fixed point theorems.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Required prior knowledge: The first part, B1, of FMAA05 Calculus in one variable

The number of participants is limited to: No

The course might be cancelled: If the number of applicants is less than 5.

- Amol Sasane: The How and Why of One Variable Calculus. Wiley, 2015, ISBN: 9781119043386. Also available as an e-book via the Mathematics library.

Course coordinator: Anders Holst, studierektor@math.lth.se

Course coordinator: Tomas Persson, tomasp@maths.lth.se

Course administrator: Studerandeexpeditionen, expedition@math.lth.se

Course homepage: http://www.maths.lth.se/course/intrreellanal/