Course Unit

• X-rays
• Radon transform
• Back projection
• Central slice theorem
• Filtered back projection formula
• Discrete image reconstruction
• Algebraic reconstruction techniques
• Kernel-based image reconstructions

• Fluid dynamical models (Euler, Navier-Stokes, vortex models),
• Traffic flow models,
• Theory of elasticity,
• Hyperbolic conservation laws,
• Image processing models (nonlinear diffusion filter, shock filter),
• Models for pattern formation (reaktion-diffusion equations, Turing instability),
• Evolution of thin films,
• Collective behavior (kinetic equations)

• Introduction to semiconductor physics and devices:

In this course we will learn how the quantum mechanics of solids and transport has been harnessed to build the Digital Age. We will explore the physics of semiconductors and semiconductor devices and the role they play in modern technology. We will also lay the ground-work for more advanced discussions of how computational techniques and simulation can be used to push knowledge in this field forward to new horizons.

* Basic Structure of Crystals and Solids, Quantum Mechanics of Solids, Physics of Semiconductors, Transport in Semiconductors, PN junction, PN diode, PN Junctions and Modern Technology (LEDs, Photovoltaics, etc.), MOS transistor, MOS capacitor, MOSFETs and Modern Technology (VLSI, IGFET Sensors, etc.), Metal/semiconductor interfaces, Heterostructures and Modern Technology (Schottky Diodes, 2D-FETs, etc.)

• Theory, modelling and simulation of MEMS & NEMS:

The design of micro- and nanoelectromechanical systems (MEMS/NEMS) is a highly interdisciplinary field which reflects in the variety of topics of this course. Starting from an introduction to continuum mechanics and piezoelectricity we investigate different aspects of the mechanics of basic MEMS/NEMS structures like membranes and beams. By understanding the interaction of MEMS/NEMS with their environment, we are able to understand the outstanding performance of MEMS/NEMS sensors for mass and fluid sensing. Another important aspect for the modelling of MEMS/NEMS is the representation of MEMS/NEMS with discrete lumped element models and we discuss the most important discrete models. For quantitative predictions often numerical methods need to be employed for which the FEM is the most known. We discuss the fundamental theory of the FEM and its limitations. Using the above theory, we study example applications like reference oscillators or fluid sensors. Additionally, we take a look at novel concepts like phononic crystals or quantum MEMS/NEMS. 

Frequency domain models of Linear Systems: Laplace Transform, Transfer Functions, Block diagrams.
Time domain models of Linear Systems: State space representation.
BIBO stability.
Control specifications for transient and steady-state responses. Polynomial and sinusoidal disturbances rejection.
Digital control: Z-Transform, discretization of continuous-time linear systems, finite-time response, deadbeat response.
Analysis and control design using the eigenvalues assignment: controllability, observability, the separation principle.
Controller design using MATLAB.