MathMods :: Joint MSc

Sem2 Numerics UHH

Sem2 Numerics UHH

Numerics  @  UHH  30 ECTS credits

The second semester in Hamburg is characterized by a stronger "engineering oriented" perspective, in that it provides optional units at the interface of Computer Science and case studies of industrial applications of mathematics.



  • Numerical approximation of PDEs by finite differences and finite volumes [6 credits]

    Numerical approximation of PDEs by finite differences and finite volumes

    • ECTS credits 6
    • Semester 1
    • University University of Hamburg
    • Objectives

       

      The overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for non-linear systems of conservation laws, particularly for problems involving shock waves.

    • Topics

       

      Numerical methods for linear equations. Computing discontinuous solutions. Conservative methods for non-linear problems. Godunov's methods. Approximate Riemann solvers. Nonlinear stability. High resolution methods. Semi-discrete methods.


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  • Numerical methods for PDEs - Galerkin Methods [6 credits]

    Numerical methods for PDEs - Galerkin Methods

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      In this course the basic principles of the FE element method applied to the numerical treatment of elliptic PDEs are considered. Successful applicants will be able to use the FE method as analytic and numerical tool for the mathematical investigation of l

    • Topics

       

      Topics include construction of FE spaces, derivation and numerical solution of the resulting linear algebra systems, error analysis in Sobolev spaces including interpolation estimates, basic principles of residual based a posteriori error analysis.


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  • Advanced Optimisation [6 credits]

    Advanced Optimisation

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      Minimization of nonlinear functionals on infinite dimensional spaces subject to constraints. Solution algorithms for constrained and unconstrained nonlinear optimization problems. Aspects of numerical approximation and implementation. Convex optimization. Nonsmooth optimization.

    • Topics

       

      Existence and uniqueness of solutions. Necessary and sufficient optimality conditions. Constraint qualifications. Kuhn-Tucker theorems. Steepest descent and Newton-type methods for unconstrained optimization, SQP methods, penalty methods and interior point methods for constrained optimization. Semismooth Newton and Primal-Dual Active set methods for nonsmooth problems.


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  • Scientific computing [6 credits]

    Scientific computing

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      ...

    • Topics

       

      ...


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  • Modelling camp [2 credits]

    Modelling camp

    • ECTS credits 2
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      In this seminar we face the students with real world problems. We discuss the interface between the real world  industrial problems and applied mathematics.

    • Topics

       

      A series of 22 small real world industrial problems where mathematics has been applied successfully.


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  • German language and culture for foreigners (level A1) [4 credits]

    German language and culture for foreigners (level A1)

    • ECTS credits 4
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      - To understand sentences and frequently used expressions related to familiar everyday expressions, university life and its requirements.
      - To describe your place of residence and the city of Hamburg
      - To complete simple forms
      - To impart basic grammar structures and vocabulary
      - To enable to read and understand.

    • Topics

       

      - To introduce sb to sb + talking about yourself; alphabet, spelling, so called "w-questions", numbers (1-1 Mio), time, days of the week, pronunciation

      - Simple role plays

      - Grammar: word order, construction of German sentences , affirmative sentence, questions, regular verbs → present tense, auxiliary verbs "haben" and "sein", pronouns (Nominativ ), negative answer to a question "nicht" and "kein"

       


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Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

Hamburg University of Technology, Germany (TUHH)

Institute of Mathematics
Schwarzenberg-Campus 3, Building E-10
D-21073 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

Vienna Univ. of Technology, Austria (TUW)

Technische Universität Wien
Institute of Analysis & Scientific Computing
Wiedner Hauptstr. 8, 1040 Vienna - Austria

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