100211 Analysis I

Course offering details

Instructors: Prof. Dr. Götz Pfander

Type: Lecture

Org-unit:

Course Name Abbreviation: Analysis I

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
Analysis I/II is one of the fundamental courses in the mathematical education (together with Linear Algebra I/II). Its goal is to develop calculus in a rigorous manner and in sufficient generality to prepare the student for advanced work in mathematics. At the same time, the content is chosen so that students arrive quickly at central concepts which are used in essentially all mathematics courses, and which are needed in the exact sciences.

The Analysis sequence begins with a quick review of natural, rational and real numbers (which are assumed as known), and introduces the field of complex numbers. The axiom of completeness distinguishes the real numbers from the rationals and marks the beginning of Analysis.

Metric spaces are introduced and used to define continuity and convergence in a general framework. The intermediate and maximal value theorems for real numbers are discussed as consequences of connectedness and compactness on metric spaces.

Another important subject are sequences and series of complex numbers and their convergence criteria. In particular, the complex exponential series is discussed together with its offspring, the sine and cosine functions.

Finally, differentiability of functions on the real line is introduced, together with Taylor approximation.

This course has no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this class in their first semester. However, a familiarity with mathematical reasoning and proof (e.g.\ proof by induction or by contradiction), such as introduced in 110100 General Mathematics and Computational Science, is required.

Additional Information:
All participants are strongly encouraged to fill in the teaching evaluation.

Literature
Primary Text
Required Reading (To view a list click a category.)
Recommended Reading (To view a list click a category.)
Appointments
Date From To Room Instructors
1 Tue, 7. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
2 Th, 9. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
3 Tue, 14. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
4 Th, 16. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
5 Tue, 21. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
6 Th, 23. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
7 Tue, 28. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
8 Th, 30. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
9 Tue, 5. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
10 Th, 7. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
11 Tue, 12. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
12 Th, 14. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
13 Th, 21. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
14 Tue, 26. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
15 Th, 28. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
16 Tue, 2. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
17 Th, 4. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
18 Tue, 9. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
19 Th, 11. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
20 Tue, 16. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
21 Th, 18. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
22 Tue, 23. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
23 Th, 25. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
24 Tue, 30. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
25 Th, 2. Dec. 2010 11:15 12:30 East Hall 4 Prof. Dr. Götz Pfander
26 Tue, 7. Dec. 2010 08:15 09:30 East Hall 4 Prof. Dr. Götz Pfander
27 Mon, 13. Dec. 2010 16:00 18:00 East Hall 4 Prof. Dr. Götz Pfander
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
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Instructors
Prof. Dr. Götz Pfander