100211 Analysis I

Course offering details

Instructors: Prof. Dr. Peter Oswald

Type: Lecture

Org-unit:

Course Name Abbreviation: Analysis I

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Exam (40%)
Home Work (30%)
Midterm Exam (30%)

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
  • Mathematical analysis, Vol. 1
  • Principles of Mathematical Analysis
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 Th, 3. Sep. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
2 Tue, 8. Sep. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
3 Th, 10. Sep. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
4 Tue, 15. Sep. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
5 Th, 17. Sep. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
6 Tue, 22. Sep. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
7 Th, 24. Sep. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
8 Tue, 29. Sep. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
9 Th, 1. Oct. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
10 Tue, 6. Oct. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
11 Th, 8. Oct. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
12 Th, 15. Oct. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
13 Tue, 20. Oct. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
14 Th, 22. Oct. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
15 Tue, 27. Oct. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
16 Th, 29. Oct. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
17 Tue, 3. Nov. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
18 Th, 5. Nov. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
19 Tue, 10. Nov. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
20 Th, 12. Nov. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
21 Tue, 17. Nov. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
22 Th, 19. Nov. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
23 Tue, 24. Nov. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
24 Th, 26. Nov. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
25 Tue, 1. Dec. 2009 08:15 09:30 East Hall 4 Prof. Dr. Peter Oswald
26 Th, 3. Dec. 2009 11:15 12:30 East Hall 4 Prof. Dr. Peter Oswald
Course specific exams
Description Date Instructors Mandatory
1. Final Exam Th, 10. Dec. 2009 09:00-11:00 Prof. Dr. Peter Oswald No
1. Home Work No Date No
1. Midterm Exam Time tbd 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. Peter Oswald