Analysis 1
Module MA0001
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of WS 2019/20
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
| available module versions | |||
|---|---|---|---|
| SS 2021 | WS 2020/1 | SS 2020 | WS 2019/20 |
Basic Information
MA0001 is a semester module in German language at Bachelor’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Further Modules from Other Disciplines
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 270 h | 135 h | 9 CP |
Content, Learning Outcome and Preconditions
Content
Basic proof techniques including mathematical induction. Basic notions and calculus rules for functions and sets including inverse functions. Trigonometric and exponential functions (tied to the viewpoint of G8) and their inverses as examples.
Real numbers (axiomatic, not derived from Q, field axioms are assumed to be given from the linear algebra course), in particular the notion of supremum and the completeness axiom.
Complex numbers. Notion of limit, convergence of sequences.
Series: Convergence, absolute convergence, quotient criterion.
Analysis of a function of a single variable: Continuity, derivative and integral (calculus and notions), Taylor expansion including those of trigonometric and exponential functions. Explicit solutions of simple ordinary differential equations.
Real numbers (axiomatic, not derived from Q, field axioms are assumed to be given from the linear algebra course), in particular the notion of supremum and the completeness axiom.
Complex numbers. Notion of limit, convergence of sequences.
Series: Convergence, absolute convergence, quotient criterion.
Analysis of a function of a single variable: Continuity, derivative and integral (calculus and notions), Taylor expansion including those of trigonometric and exponential functions. Explicit solutions of simple ordinary differential equations.
Learning Outcome
Nach dem erfolgreichen Abschluss des Moduls besitzen die Studierenden Rechenfertigkeiten im Reellen und Komplexen. Sie verfügen über eine anschauliche Vorstellung und ein theoretisches Verständnis von Funktionen einer reellen Veränderlichen. Sie kennen Grundbegriffe (z.B. Grenzwert, Stetigkeit, Ableitung, Integral) und grundlegende Methoden (z.B. Bestimmung des Konvergenzverhaltens von Reihen, Taylorapproximation, Separationsmethode zur Lösung einfacher Differentialgleichungen) der Analysis und sind in der Lage, die erworbenen Kenntnisse erfolgreich auf einfache Problemstellungen anzuwenden.
Preconditions
knowledge of natural numbers, integers and rational numbers
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 5 | Analysis 1 [MA0001] | Friesecke, G. Kruse, H. |
Tue, 12:00–13:30, MI HS1 Fri, 08:30–10:00, Interims I 101 Mon, 14:15–15:45, MI HS1 and singular or moved dates |
eLearning |
| UE | 2 | Analysis 1 (Exercise Session) [MA0001] | Friesecke, G. Kruse, H. | dates in groups | |
| UE | 2 | Analysis 1 (Central Exercise Session) [MA0001] | Friesecke, G. Kruse, H. |
Mon, 12:15–13:45, PH HS1 |
Learning and Teaching Methods
lecture, exercise module
Media
blackboard, assignments
Literature
K. Königsberger, Analysis 1, 6. Auflage, Springer 2003.
W. Rudin, Principles of Mathematical Analysis, 2nd ed, McGraw Hill, 1964.
W. Rudin, Principles of Mathematical Analysis, 2nd ed, McGraw Hill, 1964.