ECTS Credits: 8   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0641

Unit Coordinator: Dirk Praetorius, Claudia Blaas-Schenner

Aims:

• Scientific programming in mathematics:

    formulate (certain) mathematical problems in algorithmic form,

    implement these elementary algorithms in C and C++,

    explain the difference between imperative and object-oriented programming,

    present and explain own solutions, and

    constructively discuss and analyze own solutions as well as those of other students.

• Programming with MATLAB:

    design, debug and test programs in the MATLAB language

    solve easy to moderately difficult problems in statistics and applied mathematics using MATLAB

•  Basics of Parallel Computing:

    Understand and express asymptotic running time and work of parallel algorithms

    Understand parallel algorithm using the PRAM model with respect to running time and work

    Understand and appreciate characteristics of thread models for parallel computing

    Read and write programs in OpenMP

    Read and write programs in MPI

    Understand and appreciate task parallel models for parallel computing

Content:

• Scientific programming in mathematics:

Object oriented design and programming in C++: Representation of integer and floating point numbers. Conditioning of given problems. Computational cost of algorithms. Variables and standard data types. Pointers. Functions and recursion. Call by value vs. call by reference. Loops, Objects and classes (resp. structures), Operator overloading, Inheritance and virtual. 

• Programming with MATLAB:

MATLAB syntax (command- and object-oriented), graphical representations, problems in linear algebra, optimization and statistics, solution of ordinary differential equations by functions in the various toolboxes.

• Basics of Parallel Computing:

Motivation and goals of parallel computing, parallel computer architectures, programming models, performance measurement and analysis, introduction to programming paradigms such as MPI (Message Passing Interface), Pthreads, and OpenMP. Other aspects and languages for programming multi-core processors.

Pre-requisites:

• Programming with MATLAB:

Basic knowledge of higher mathematics (functions, linear algebra, ordinary differential equations)

• Basics of Parallel Computing:

Knowledge of programming languages, computer architectures, operating systems. Basic Algorithms and Datastructures (asymptotic worst-case analysis). Programming skills in C, C++, Fortran or Java.

Reading list:

• Scientific programming in mathematics:

lecture notes

• Programming with MATLAB:

Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB

Brian Hahn, Essential MATLAB for Engineers and Scientists

Stormy Attaway, Matlab: A Practical Introduction to Programming and Problem Solving

•  Basics of Parallel Computing:

    Rauber, Rünger: Parallel programming. Second Edition, Springer 2013.

    Schmidt, Gonzalez-Dominguez, Hundt, Schlarb: Parallel Programming. Concepts and Practice. Morgan Kaufmann 2018.

ECTS Credits: 6   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0371

Unit Coordinator: Kevin Sturm, Phillip Baumann

Aims:

To understand, analyze, formulate and graphically or mathematically solve basic static and dynamic optimization problems. Students will know about the theory, the mathematically principles and various methods for an exact or iterative solution of optimization problems.

They can moreover differentiate between unconstrained and constrained optimization problems and they can select and apply the specifically appropriate solution methods. 

Content:

• Fundamentals of optimization: existence of minima and maxima, gradient, Hessian, convexity, convergence
• Unconstrained static optimization: optimality conditions, computer-aided optimization, line search methods, choice of the step length, principle of nested intervals, Armijo condition, Wolfe condition, gradient method, Newton method, conjugate gradient method, Quasi-Newton method, Gauss-Newton-method, trust region method, Nelder-Mead method
• Static optimization with constraints: equality and inequality constraints, sensitivity considerations, active set method, gradient projection method, reduced gradient method, penalty and barrier functions, sequential quadratic programming (SQP), local SQP, globalization of SQP

Pre-requisites:

• Analysis,
• Linear algebra,
• Numerical mathematics,
• Differential equations.

Reading list:

• lecture notes,
• J. Macki und A. Strauss: Introduction to Optimal Control Theory. New York, Springer, 1982.
• Jorge Nocedal, Stephen J. Wright: Numerical Optimization, Springer 2006

ECTS Credits: 6   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0639

Unit Coordinator: Jens Markus Melenk, Alexander Rieder

Aims:

Being able to check if the numerical solution of an ordinary differential equation makes sense.

Moreover, depending on th inherent structure of the differential equation, they know what integrator should be chosen.

Content:

Initial- and boundary value problems for ordinary and partial differential equations: One-step and multi-step methods, adaptivity, structure perserving integrators.

Introduction to numerical methods for partial differential equations.

Pre-requisites:

Analysis, linear algebra, numerical mathematics.

Knowledge of ODEs is advantageous but not necessary.

Reading list:

Lecture notes.

ECTS Credits: 7   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |   Language: English   |   Code: DT0640

Unit Coordinator: Joachim Schöberl, Edoardo Bonetti

Aims:

• Solve stationary partial differential equations numerically
• Analyse the quality of numerical solutions
• Select proper methods and implement them in a computer programme

Content:

• Variational formulations
• Sobolev spaces, H(div), H(curl)
• Finite element spaces (h, p, hp)
• Mixed formulations
• Discontinuous Galerkin methods
• Time-dependent problems

Pre-requisites:

Analysis, linear algebra, numerical mathematics.

Reading list:

• Lecture notes,
• Dietrich Braess: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, 2007
• Cleas Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, 1987, Dover 2009
• Susanne Brenner & Ridgway Scott: The Mathematical Theory of Finite Elements, Springer 2008
• Alexandre Ern & Jean-Luc Guermond: Theory and Practice of Finite Elements, Springer, 2010 

ECTS Credits: 3   |   Semester: 2   |   Year: 1   |   Campus: Vienna University of Technology   |      |   Code: DT0663

Unit Coordinator: Innes Institue

Aims:

Learn German at level A1 (speak, read, write)

Content:

• Learn German at level A1 (speak, read, write)
• Social & cultural program, waltz workshop

Reading list:

Lecture notes by Innes