Module Handbook

  • Dynamischer Default-Fachbereich geändert auf BI

Module BI-BSCBI-018-M-4

Höhere Mathematik für Bauingenieure III - Differentialgleichungen (M, 5.0 LP)

Module Identification

Module Number Module Name CP (Effort)
BI-BSCBI-018-M-4 Höhere Mathematik für Bauingenieure III - Differentialgleichungen 5.0 CP (150 h)

Basedata

CP, Effort 5.0 CP = 150 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [DE] German
Module Manager
Lecturers
Area of study [BI-SDT] Statik und Dynamik der Tragwerke
Reference course of study [BI-82.17-SG] B.Sc. Civil Engineering
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-00-031-K-1
Higher Mathematics; Differential Equations (for Engineering Students)
P 42 h 78 h
U-Schein
ja PL1 4.0 WiSe
1U BI-SDT-WS009VU-K-1
Anwendung mathematischer Methoden im Bauwesen
P 7 h 23 h
U-Schein
- no 1.0 WiSe
  • About [MAT-00-031-K-1]: Title: "Higher Mathematics; Differential Equations (for Engineering Students)"; Presence-Time: 42 h; Self-Study: 78 h
  • About [MAT-00-031-K-1]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained. It is a prerequisite for the examination for PL1.
  • About [BI-SDT-WS009VU-K-1]: Title: "Anwendung mathematischer Methoden im Bauwesen"; Presence-Time: 7 h; Self-Study: 23 h
  • About [BI-SDT-WS009VU-K-1]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: written exam (Klausur) (45-60 Min.)
  • Examination Frequency: each semester
  • Examination number: 81016 ("Higher Mathematics: Differential Equations")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Basic concepts for the treatment of ordinary and partial differential equations:

A. Ordinary differential equations:

  • first-order differential equations: existence and uniqueness, first-order autonomous differential equations, separation approach, variation of constants, explicitly solvable cases, initial value problems;
  • linear differential equations: homogeneous linear systems, matrix-exponential function, variation of constants, differential equations of nth order.

B. Partial differential equations:

  • classification and well-posedness of 2nd order partial differential equations;
  • wave equation, Poisson's equation, Fourier transform;
  • solution methods: separation approach, Fourier transformation.

C. Numerical solution of differential equations:

  • single step method (implicit/explicit);
  • Runge-Kutta method;
  • step size control.
Übungsbeispiele mit typischen Problemstellungen aus dem Bauingenieurwesen werden vorgestellt und mit Hilfe geeigneter Software am Computer gelöst.

Competencies / intended learning achievements

Mit erfolgreichem Abschluss des Moduls werden die Studierenden in der Lage sein,
  • Probleme aus Wissenschaft und Technik mittels mathematischer Methoden lösen
  • ausgewählte Problemstellungen aus dem Bauingenieurwesen in mathematische Formulierungen umzusetzen und diese mit Hilfe von geeigneter Software am Computer zu lösen

Literature

Literatur wird in den Lehrveranstaltungen angegeben

Materials

Zugang zu Vorlesungsskripten und weiteren Lernmaterialien wird in den Lehrveranstaltungen mitgeteilt

Registration

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [BI-BSCBI-018-M-4]

Course of Study Section Choice/Obligation
[BI-82.17-SG] B.Sc. Civil Engineering Fachspezifische Vertiefung, Schwerpunkt: Konstruktiver Ingenieurbau (KIB) [WP] Compulsory Elective