SF2713
Credits: 7,5
ECTS Credits: 7,5
Level: C
Grading: A-F
Language: Engelska / English
Compulsory for
TMTHM1
Time
Period 1, 2
Lessons 54h
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Foundations of Analysis
Introductory course in analysis.
Aim
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.
Syllabus
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.)
Prerequisites
Analysis corresponding to SF1602 and SF1603 or SF1600 and SF1601 and
preferably also complex analysis, differential equations and transforms
corresponding to SF1628 and SF1629.
Requirements
Written examination. Possibly partial examination (optional) during the
course.
Required reading
* Rudin, Walter, "Principles of mathematical analysis".
or
* Pugh, Charles Chapman, "Real mathematical analysis".
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