Module Handbook

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Module MAT-81-31-M-7

Theory of Hyperbolic Conservation Laws (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-31-M-7 Theory of Hyperbolic Conservation Laws 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
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 MAT-81-31-K-7
Theory of Hyperbolic Conservation Laws
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-31-K-7]: Title: "Theory of Hyperbolic Conservation Laws"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86445 ("Theory of Hyperbolic Conservation Laws")

Evaluation of grades

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


Contents

  • introduction to hyperbolic conservation laws,
  • analytical statements for scalar hyperbolic equations,
  • analytical statements for systems of hyperbolic conservation equations (in particular, WaveFrontTracking).

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the analytical statements about hyperbolic conservation laws as well as the reasons for the limitations of possible statements. Moreover, the students are able to independently apply the techniques taught in the lecture (e.g. the Wave Front Tracking). They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of statements.

Literature

  • A. Bressan: Hyperbolic conservation laws: an illustrated tutorial; in: Modelling and Optimisation of Flows on Networks,
  • A. Bressan: Hyperbolic Systems of Conservation Laws - The One-dimensional Cauchy Problem.

References to Module / Module Number [MAT-81-31-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)