100211 Analysis I

Course offering details

Instructors: Prof. Dr. Dierk Schleicher

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.

Literature
Primary Text
  • Analysis I - Text and Readings in Mathematics
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, 4. Sep. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
2 Th, 6. Sep. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
3 Tue, 11. Sep. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
4 Th, 13. Sep. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
5 Tue, 18. Sep. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
6 Th, 20. Sep. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
7 Tue, 25. Sep. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
8 Th, 27. Sep. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
9 Tue, 2. Oct. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
10 Th, 4. Oct. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
11 Tue, 9. Oct. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
12 Th, 11. Oct. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
13 Tue, 16. Oct. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
14 Th, 18. Oct. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
15 Th, 25. Oct. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
16 Tue, 30. Oct. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
17 Th, 1. Nov. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
18 Tue, 6. Nov. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
19 Th, 8. Nov. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
20 Tue, 13. Nov. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
21 Th, 15. Nov. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
22 Tue, 20. Nov. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
23 Th, 22. Nov. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
24 Tue, 27. Nov. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
25 Th, 29. Nov. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
26 Tue, 4. Dec. 2012 08:15 09:30 East Hall 4 Prof. Dr. Dierk Schleicher
27 Th, 6. Dec. 2012 11:15 12:30 East Hall 4 Prof. Dr. Dierk Schleicher
28 Tue, 18. Dec. 2012 09:00 11:00 Lecture Hall Research III Prof. Dr. Dierk Schleicher
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
2. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Prof. Dr. Dierk Schleicher