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5954: Mathematical Analysis ( efterår 2010 - 10 ECTS )

Rammer for udbud

  • Uddannelsessprog: engelsk
  • Niveau:   COURSE LEVEL:  PhD course  
  • Semester/kvarter:   SEMESTER FOR WHICH THE COURSE DESCRIPTION APPLIES: Autumn 2010  
  • Timer per uge:   NUMBER OF HOURS PER WEEK: 4 hours and 1 problem session per week in 10 weeks (from week 38-49)  
  • Deltagerbegrænsning:
  • Undervisningssted: Århus
  • Hovedområde: Det Samfundsvidenskabelige Fakultet
  • Udbud ID: 23369

Formål

 

LEARNING OBJECTIVES:  The objective of the course is to give the participants a basic knowledge of the notions and methods of mathematical analysis with emphasis on arguments and rigorous mathematical proofs. At the end of the course, the participants should be able to give rigorous proofs of elementary statements involving metric spaces, limits, continuity, differentiability and series and sequences of functions defined on Euclidian or metric spaces.

 

Indhold

 

COURSE DESCRIPTION: The course gives a rigorous definition of real and complex numbers and treats the fundamental notions of mathematical analysis such as: finite dimensional spaces, basic topology and metric spaces, limits and continuity, derivatives of functions of one or several variables, sequences and series of functions, and integral notions.

 

 

COURSE SUBJECT AREAS: Real and complex numbers and finite dimensional spaces, basic topology, metric spaces, limits and continuity, derivatives of functions of one or several variables, sequences and series of functions, and integral notions.

 

Faglige forudsætninger

Underviser

 

LECTURER: Jørgen Hoffmann-Jørgensen

 

Undervisnings- og arbejdsform

 

TEACHING METHOD: Lectures and take-home problem sets

 

 

TEACHING LANGUAGE: English

 

Litteratur

 

LITERATURE: Textbook: Rudin, Walter. Principles of Mathematical Analysis , 3. edition, Ed. McGraw-Hill, 1976. Chap.1 p.1-17 (not the Appendix), Chap.2 p.24-43, Chap.3 p.47-75 (not Sec.3.52-3.55), Chap.4 p.83-95 (not Sec.4.28-4.31), Chap.5 p.103-113, Chap.7 p.143-161 (not Sec.7.27-7.33).

Lecture Notes: Hoffmann-Jørgensen, Jørgen. Supplementary Notes to Rudin's book:

Principles of Mathematical Analysis. p.1-43

 

Bedømmelse

  • Skriftlig, bedømt efter 7-skala med intern censur
  • 5 xxxxx

 

FORM OF ASSESSMENT: A 4-hour written final exam

 

EXAMINATION AIDS ALLOWED: All - except any means of electronic communication including calculators, mobile phones and PCs.