100211 Analysis I

Course offering details

Instructors: Prof. Dr. Daniel Meyer

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 and II is one of the fundamental courses in the mathematical education
(together with Linear Algebra I and 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. The complex exponential and trigonometric functions are defined.
Metric spaces are introduced and used to define continuity and convergence in a general
framework. The Bolzano-Weierstraß and the Heine-Borel theorems are proved. The intermediate
and maximal value theorems for functions on the real line are discussed as consequences
of connectedness and compactness on metric spaces. Sequences of functions are discussed, in
particular uniform convergence, as well as the continuity, differentiability, integrability of the
limit function.
Differentiability of functions on the real line is introduced. The mean value theorem and
Taylor’s theorem is discussed.
The Riemann integral in one variable is introduced. The relation between the derivative and
the integral, i.e., the fundamental theorem of calculus is proved.
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 General Mathematics and Computational Science I, is required.

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, 2. Sep. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
2 Th, 4. Sep. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
3 Tue, 9. Sep. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
4 Th, 11. Sep. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
5 Tue, 16. Sep. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
6 Th, 18. Sep. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
7 Tue, 23. Sep. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
8 Th, 25. Sep. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
9 Tue, 30. Sep. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
10 Th, 2. Oct. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
11 Tue, 7. Oct. 2014 08:15 09:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
12 Th, 9. Oct. 2014 11:15 12:30 Research I, Seminar Room 120 Prof. Dr. Daniel Meyer
13 Tue, 14. Oct. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
14 Th, 16. Oct. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
15 Th, 23. Oct. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
16 Tue, 28. Oct. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
17 Th, 30. Oct. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
18 Tue, 4. Nov. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
19 Th, 6. Nov. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
20 Tue, 11. Nov. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
21 Th, 13. Nov. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
22 Tue, 18. Nov. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
23 Th, 20. Nov. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
24 Tue, 25. Nov. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
25 Th, 27. Nov. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
26 Tue, 2. Dec. 2014 08:15 09:30 East Hall 2 Prof. Dr. Daniel Meyer
27 Th, 4. Dec. 2014 11:15 12:30 East Hall 2 Prof. Dr. Daniel Meyer
28 Fri, 12. Dec. 2014 16:00 18:00 Lecture Hall Research II Prof. Dr. Daniel Meyer
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 > Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Prof. Dr. Daniel Meyer