19202801 Lecture

# SoSe 21: Analysis I

## Kivanc Ersoy

Content: This is the first part of a three semester introduction into the basic mathematical field of Analysis. Differential and integral calculus in a real variable will be covered.
Topics:

1. fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
2. numbers, induction, calculations in R, C
3. arrangement of R, maximum and minimum, supremum and infimum of real sets, supremum / infimum completeness of R, absolute value of a real number, Q is dense in R
4. sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
5. topological aspects of R, open, closed, and compact real sets
6. sequences of functions, series of functions, power series
7. properties of functions, boundedness, monotony, convexity
8. continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
9. differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
10. elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
11. beginnings of integral calculus

Detailed Information can be found on the Homepage of 19202801 Analysis I.

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Literature:

• Bröcker, Theodor: Analysis 1, Spektrum der Wissenschaft-Verlag.
• Forster, Otto: Analysis 1, Vieweg-Verlag.
• Spivak, Michael: Calculus, 4th Edition.

Viele Analysis Bücher sind auch über die Fachbibliothek der FU Berlin elektronisch verfügbar.

Bei Schwierigkeiten mit den Grundbegriffen Menge, Abbildung etc. ist die folgende Ausarbeitung empfehlenswert:

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### 26 Class schedule

Thu, 2021-07-08 10:00 - 12:00
Klausur

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 02

Tue, 2021-10-05 14:00 - 16:00
Nachklausur

Lecturers:
PD Dr. Kivanc Ersoy

Location:
T9/Gr. Hörsaal (Takustr. 9)

Regular appointments

Tue, 2021-04-13 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-04-20 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-04-27 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-05-04 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-05-11 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-05-18 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-05-25 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-06-01 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-06-08 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-06-15 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-06-22 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-06-29 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-07-06 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Tue, 2021-07-13 10:00 - 12:00
Analysis I (Serientermin 1)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-04-15 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-04-22 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-04-29 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-05-06 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-05-20 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-05-27 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-06-03 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-06-10 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-06-17 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-06-24 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-07-01 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05

Thu, 2021-07-15 10:00 - 12:00
Analysis I (Serientermin 2)

Lecturers:
PD Dr. Kivanc Ersoy

Location:
Virtueller Raum 05