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Lecture
SoSe 23: Analysis I
Claudia Schillings
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
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Suggested reading
Passende Literatur wird in der Vorlesung bekanntgegeben.
26 Class schedule
Additional appointments
Thu, 2023-07-20 10:00 - 12:00Klausur
Tue, 2023-08-29 10:00 - 12:00
Nachklausur
Regular appointments
Tue, 2023-04-18 10:00 - 12:00
Analysis I
Tue, 2023-04-25 10:00 - 12:00
Analysis I
Tue, 2023-05-02 10:00 - 12:00
Analysis I
Tue, 2023-05-09 10:00 - 12:00
Analysis I
Tue, 2023-05-16 10:00 - 12:00
Analysis I
Tue, 2023-05-23 10:00 - 12:00
Analysis I
Tue, 2023-05-30 10:00 - 12:00
Analysis I
Tue, 2023-06-06 10:00 - 12:00
Analysis I
Tue, 2023-06-13 10:00 - 12:00
Analysis I
Tue, 2023-06-20 10:00 - 12:00
Analysis I
Tue, 2023-06-27 10:00 - 12:00
Analysis I
Tue, 2023-07-04 10:00 - 12:00
Analysis I
Tue, 2023-07-11 10:00 - 12:00
Analysis I
Tue, 2023-07-18 10:00 - 12:00
Analysis I
Thu, 2023-04-20 10:00 - 12:00
Analysis I
Thu, 2023-04-27 10:00 - 12:00
Analysis I
Thu, 2023-05-04 10:00 - 12:00
Analysis I
Thu, 2023-05-11 10:00 - 12:00
Analysis I
Thu, 2023-05-25 10:00 - 12:00
Analysis I
Thu, 2023-06-01 10:00 - 12:00
Analysis I
Thu, 2023-06-08 10:00 - 12:00
Analysis I
Thu, 2023-06-15 10:00 - 12:00
Analysis I
Thu, 2023-06-22 10:00 - 12:00
Analysis I
Thu, 2023-06-29 10:00 - 12:00
Analysis I
Thu, 2023-07-06 10:00 - 12:00
Analysis I
Thu, 2023-07-13 10:00 - 12:00
Analysis I