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Mathematik 2 für MEB/MM
(2018)
Vektorrechnung: Darstellung von Vektoren, Komponenten, Einheitsvektor, Addition, Subtraktion, Projektion, Skalarprodukt, Kreuzprodukt, Geraden, Ebenen Lineare Algebra: Darstellung, Rechnen mit Matrizen und Vektoren, Drehmatrix, lineare Gleichungssysteme (Eliminationsverfahren GAUSS oder GAUSS-JORDAN, inverse Matrix, über- und unterbestimmte Systeme), Determinanten (Rang einer Matrix, SARRUSsche Regel, CRAMERsche Regel), Eigenwerte und Eigenvektoren einer quadratischen Matrix
Fourier-Reihen: (Fourier-Reihe, reell, komplex, beliebige Periode, punktweise Funktion), Wellen (zeitliche und räumliche Ausbreitung von Wellen, Amplitude, Frequenz, Phase)
Differentialrechnung für Funktionen von mehreren Variablen: graphische Darstellung, skalare und Vektorfelder, partielle Ableitung, Differenzial, Gradient, Kettenregeln, Fehlerfortpflanzung
Integralrechnung für Funktionen von mehreren Variablen: konstante Grenzen, Produktzerlegung, Koordinatensysteme, Polarkoordinaten, Zylinderkoordinaten, Kugelkoordinaten, Trägheitsmomente, variable Grenzen
Gewöhnliche Differentialgleichungen: Klassifikation, Anfangswerte bzw. Randbedingungen, Trennung der Veränderlichen, Variation der Konstanten, DGL mit konstanten Koeffizienten, e-Ansatz, homogene, inhomogene DGL, charakteristische Gleichung, inhomogener Lösungen, Systeme linearer DGL Laplace-Transformation: Eigenschaften, Lösung einer DGL, Korrespondenztabellen, Partialbruchzerlegung, Rücktransformation, Übertragungsfunktion
Übungsbeispiele, Beispielklausur
It is a fundamental right of every natural person to control which personal information is collected, stored and processed by whom, for what purposes and how long. In fact, many (cloud based) services can only be used if the user allows them broad data collection and analysis. Often, users can only decide to either give their data or not to participate in communities. The refusal to provide personal data results in significant drawbacks for social interaction. That is why we believe that there is a need for tools to control one's own data in an easy and effective way as protection against economic interest of global companies and their cloud computing systems (as data collector from apps, mobiles and services). Especially, as nowadays everybody is permanently online using different services and devices, users are often lacking the means to effectively control the access to their private data. Therefore, we present an approach to manage and distribute privacy settings: PRIVACY-AVARE is intended to enable users to centrally determine their data protection preferences and to apply them on different devices. Thus, users gain control over their data when using cloud based services. In this paper, we present the main idea of PRIVACY-AVARE.
Applications for the Internet of Things are becoming increasingly popular. Due to the large amount of available context data, such applications can be used effectively in many domains. By interlinking these data and analyzing them, it is possible to gather a lot of knowledge about a user. Therefore, these applications pose a threat to privacy. In this paper, we illustrate this threat by looking at a real-world application scenario. Current state of the art focuses on privacy mechanisms either for Smart Things or for big data processing systems. However, our studies show that for a comprehensive privacy protection a holistic view on these applications is required. Therefore, we describe how to combine two promising privacy approaches from both categories, namely AVARE and PATRON. Evaluation results confirm the thereby achieved synergy effects.