19202801
Lecture
Analysis I
Pavle Blagojevic
Comments
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:
- fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
- numbers, induction, calculations in R, C
- 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
- sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
- topological aspects of R, open, closed, and compact real sets
- sequences of functions, series of functions, power series
- properties of functions, boundedness, monotony, convexity
- continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
- differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
- elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
- beginnings of integral calculus
Detailed Information can be found on the Homepage of 19202801 Analysis I.
closeSuggested reading
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:
- Scheerer, Hans: Brückenkurs, Skript FU Berlin 2006.
25 Class schedule
Regular appointments
Tue, 2025-04-15 10:00 - 12:00
Tue, 2025-04-22 10:00 - 12:00
Tue, 2025-04-29 10:00 - 12:00
Tue, 2025-05-06 10:00 - 12:00
Tue, 2025-05-13 10:00 - 12:00
Tue, 2025-05-20 10:00 - 12:00
Tue, 2025-05-27 10:00 - 12:00
Tue, 2025-06-03 10:00 - 12:00
Tue, 2025-06-10 10:00 - 12:00
Tue, 2025-06-17 10:00 - 12:00
Tue, 2025-06-24 10:00 - 12:00
Tue, 2025-07-01 10:00 - 12:00
Tue, 2025-07-08 10:00 - 12:00
Tue, 2025-07-15 10:00 - 12:00
Thu, 2025-04-17 10:00 - 12:00
Thu, 2025-04-24 10:00 - 12:00
Thu, 2025-05-15 10:00 - 12:00
Thu, 2025-05-22 10:00 - 12:00
Thu, 2025-06-05 10:00 - 12:00
Thu, 2025-06-12 10:00 - 12:00
Thu, 2025-06-19 10:00 - 12:00
Thu, 2025-06-26 10:00 - 12:00
Thu, 2025-07-03 10:00 - 12:00
Thu, 2025-07-10 10:00 - 12:00
Thu, 2025-07-17 10:00 - 12:00