Real Analysis, Honours Course, 6 credits

Analys, överkurs, 6 hp

TATA34

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Jana Björn

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 124 h
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 4 Swedish Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Additional courses) 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6CIII Industrial Engineering and Management, M Sc in Engineering 7 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6KMAT Mathematics, Bachelor´s Programme 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6KMAT Mathematics, Bachelor´s Programme (Applied Mathematics) 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6KMAT Mathematics, Bachelor´s Programme (Computer Science) 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6KMAT Mathematics, Bachelor´s Programme (Mathematics) 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
6KMAT Mathematics, Bachelor´s Programme (Modelling and Optimization in Economics) 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping E
ECV = Elective / Compulsory / Voluntary

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course offered for

  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics, Bachelor´s Programme

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

A basic course in calculus and linear algebra.

Intended learning outcomes

To extend and enhance the analysis taught in the basic calculus courses as a preparation for more advanced studies in mathematics and applied subjects. In the course, the student also practices his/her ability to read and write mathematical text and, in particular, mathematical proofs. After completing the course, the student should

  • have a good understanding of the real number system and of functions of a real variable,
  • be able to cite and explain the essential definitions and theorems in real analysis,
  • be able to apply the theory to new situations,
  • be able to independently formulate and prove simple results about functions of a real variable.

Course content

The real number system, limits of sequences, series, limits of functions, continuity, differentiation, sequences and series of functions, the Riemann integral.

Teaching and working methods

Lectures.
The course runs over the entire autumn semester.

Examination

UPG1Assignments6 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Jana Björn

Course website and other links

http://courses.mai.liu.se/Lists/html/index-amne-tm.html

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 124 h

Course literature

Additional literature

Books

  • S. Abbott, (2001) Understanding Analysis
Code Name Scope Grading scale
UPG1 Assignments 6 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

Additional literature

Books

S. Abbott, (2001) Understanding Analysis

Note: The course matrix is not fully translated to English.

I U A Modules Comment
1. ÄMNESKUNSKAPER
1.1 Kunskaper i grundläggande matematiska och naturvetenskapliga ämnen
X
X
X
UPG1
I och U: Det reella talsystemet, satser om kontinuerliga funktioner, differential- och integralkalkyl, funktionsserier, Banachs fixpunktssats. A: Grundläggande differential- och integralkalkyl från envariabelanalys.
1.2 Kunskaper i grundläggande (motsvarande G1X) teknikvetenskapliga ämnen
1.3 Fördjupade kunskaper (motsvarande G2X), metoder och verktyg inom något/några teknik- och naturvetenskapliga ämnen
1.4 Väsentligt fördjupade kunskaper (motsvarande A1X), metoder och verktyg inom något/några teknik- och naturvetenskapliga ämnen
1.5 Insikt i aktuellt forsknings- och utvecklingsarbete
2. INDIVIDUELLA OCH YRKESMÄSSIGA FÄRDIGHETER OCH FÖRHÅLLNINGSSÄTT
2.1 Analytiskt tänkande och problemlösning
X
X
UPG1
Matematisk teori och problemlösning, rimlighetskontroll
2.2 Experimenterande och undersökande arbetssätt samt kunskapsbildning
X
Problemlösning
2.3 Systemtänkande
UPG1
2.4 Förhållningssätt, tänkande och lärande
X
X
UPG1
Matematisk problemlösning, rimlighetskontroll
2.5 Etik, likabehandling och ansvarstagande
3. FÖRMÅGA ATT ARBETA I GRUPP OCH ATT KOMMUNICERA
3.1 Arbete i grupp
3.2 Kommunikation
X
UPG1
Skriftligt och muntligt
3.3 Kommunikation på främmande språk
X
Engelskspråkig kurslitteratur
4. PLANERING, UTVECKLING, REALISERING OCH DRIFT AV TEKNISKA PRODUKTER OCH SYSTEM MED HÄNSYN TILL AFFÄRSMÄSSIGA OCH SAMHÄLLELIGA BEHOV OCH KRAV
4.1 Samhälleliga villkor, inklusive ekonomiskt, socialt och ekologiskt hållbar utveckling för kunskapsutveckling
4.2 Företags- och affärsmässiga villkor
4.3 Att identifiera behov samt strukturera och planera utveckling av produkter och system
4.4 Att konstruera produkter och system
4.5 Att realisera produkter och system
4.6 Att ta i drift och använda produkter och system
5. PLANERING, GENOMFÖRANDE OCH PRESENTATION AV FORSKNINGS- ELLER UTVECKLINGSPROJEKT MED HÄNSYN TILL VETENSKAPLIGA OCH SAMHÄLLELIGA BEHOV OCH KRAV
5.1 Samhälleliga villkor, inklusive ekonomiskt, socialt och ekologiskt hållbar utveckling
5.2 Ekonomiska villkor för kunskapsutveckling
5.3 Att identifiera behov samt strukturera och planera forsknings- eller utvecklingsprojekt
5.4 Att genomföra forsknings- eller utvecklingsprojekt
5.5 Att redovisa och utvärdera forsknings- eller utvecklingsprojekt

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