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SF2713 Foundations of Analysis 7.5 credits

Analysens grunder

Introductory course in analysis.

  • Educational level

    Second cycle

  • Academic level (A-D)

    C

  • Subject area

    Mathematics

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 12 for programme students

Autumn 13 for programme students

  • Periods

    Autumn 13 P1 (3.7 credits), P2 (3.8 credits)

  • Application code

    50733

  • Start date

    2013 week: 36

  • End date

    2014 week: 3

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Number of lectures

  • Number of exercises

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Schedule

    Schedule (new window)

  • Course responsible

    Lars Svensson

  • Part of programme

Learning outcomes

The course is a fundamental course for studies in more advanced mathematics and for studies in closely related fields.

By the end of the course the student should be able to solve problems on the different topics of the course. In particular the student should be able to

  • Understand and be able to apply basic topological concepts. Be able to state the theorems of Heine-Borel and Bolzano-Weierstrass.
  • Understand and be able to apply the concepts of continuity, convergence and derivative for functions between metric spaces. Be able to state Arzelà-Ascoli´s theorem and Weierstrass´ approximation theorem.

Course main content

Real numbers. Metric spaces. Basic topological concepts. Convergence. Continuity.

Derivative. Integral. Uniform convergence. Spaces of functions.

Banach´s fixed point theorem. Implicit and inverse mapping theorem. (Something about Lebesgue integral, alternatively something about differential forms and Stokes theorem.)

Eligibility

Analysis corresponding to SF1602 and SF1603 or SF1600 and SF1601 and preferably also complex analysis, differential equations and transforms corresponding to SF1628 and SF1629.

Literature

* Rudin, Walter, "Principles of mathematical analysis".

or

* Pugh, Charles Chapman, "Real mathematical analysis".

Examination

  • TEN1 - Examination, 7.5 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Written examination. Possibly partial examination (optional) during the course.

Offered by

SCI/Mathematics

Contact

Lars Svensson

Examiner

Lars Svensson

Version

Course plan valid from: Autumn 07.
Examination information valid from: Autumn 07.