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t.BA.XXM1.AN2.19HS (Analysis 2)
Module: Analysis 2
This information was generated on: 25 October 2024
No.
t.BA.XXM1.AN2.19HS
Title
Analysis 2
Organised by
T IAMP
Credits
4
Description
Version: 5.0 start 01 February 2025
Short description
Basic concepts and methods of differential and integral calculus of one real variable, as well as their application.
Module coordinator
Lichtensteiger Lukas (licn)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
You use the elementary integration methods: partial integration, substitution method and integration with partial fraction decomposition.
F, M
K3
You use integral calculus to calculate the length of a curve, the coordinates of a centroid, and the volume content of a rotation object.
F, M
K2
You use the rule of Bernoulli and determine the values of improper integrals with symbolic methods.
F, M
K3
You determine the convergence or divergence of a series of numbers using the quotient criterion.
F, M
K3
You determine the radius of convergence for a given power series and use operations with power series correctly.
F, M
K3
You develop a given function into a Taylor series and use it to derive approximation formulas.
F, M
K3
You determine the direction fields for ordinary differential equations and graphically determine integral curves to given initial values.
F, M
K3
You solve the initial value problem for simple linear and separable differential equations using various methods.
F, M
K3
Module contents
1. Extension of the integral calculus
Elementary integration methods (partial integration, substitution method, integration with partial fraction decomposition), applications of integral calculus, rule of Bernoulli, improper integrals
2. Power series and Taylor series
Convergence and divergence of series, power series, convergence radius, Taylor series, function approximation formulas
3. Introduction to ordinary differential equations
Graphical solution methods (direction fields, integral curves), symbolic solution methods for linear and separable differential equations
Teaching materials
Notes and exercises distributed by lecturers, Moodle
Supplementary literature
Mathematik für Ingenieure und Naturwissenschaftler, Lothar Papula, Vieweg+Teubner
Prerequisites
Mathematics of technical BM
Knowledge of the contents of the module Analysis 1
Teaching language
(X) German ( ) English
Part of International Profile
( ) Yes (X) No
Module structure
Type 3a
For more details please click on this link:
T_CL_Modulauspraegungen_SM2025
Exams
Description
Type
Form
Scope
Grade
Weighting
Graded assignments during teaching semester
regular assessments
written
max. 45 minutes each
grade
maximum 20%
End-of-semester exam
exam
written
90 minutes
grade
at least 80%
Remarks
During the first week of classes, a module agreement will be communicated which applies to all module courses and in which the exact number and scope of the graded assignments during the semester as well as the calculation method for the module grade are determined.
Legal basis
The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Note
Additional available versions:
2.0 start 01 February 2019
,
4.0 start 01 February 2022
Course: Analysis 2 - Praktikum
No.
t.BA.XXM1.AN2.19HS.P
Title
Analysis 2 - Praktikum
Note
No module description is available in the system for the cut-off date of 02 August 2099.
Course: Analysis 2 - Vorlesung
No.
t.BA.XXM1.AN2.19HS.V
Title
Analysis 2 - Vorlesung
Note
No module description is available in the system for the cut-off date of 02 August 2099.