Advanced Mathematics 1: Fundamentals: real and complex numbers, Supremum, Induction, notion of functions, mathematic notation; Linear algebra: vectors, matrices, linear equation systems, scalar and vector product, orthogonality, linear spaces, linear transformation, eigenvalues, factorise matrices (diagonalising and singular value analysis), matrix norm; Analysis: sequences, series, limits, steadiness

Advanced Mathematics 2: Analysis (1 dimension): theorems and formulae of differential calculus, extreme values, theorems and formulae of integral calculus, improper integrals (including Laplace transformation); differential equations: linear systems with constant coefficients; Analysis (multidimensional): curves, scalar and vector fields, partial derivation, gradient, total derivation, functional matrix, implicit functions, extreme value with and without side conditions, line integral and potential

Review of Mathematics; Units and Dimensions; 1D Kinematics; 2D Kinematics; Newton’s Laws; Work and Energy; Momentum; Rotation; Waves and Oscillations; Zeroth Law; Ideal Gas; Kinetic theory; Specific Heat; Thermodynamics – First Law.

Introduction; Fundamentals; Drawing of device I; Drawing of device II; Basics of dimensions; Dimensions of devices; Surface, Edge and mechanical properties; Tolerances; Fittings; Connection between devices, Forging, Casting; DIN and standard parts; Introduction to CAD

Atoms; Atomic theory; Chemical Bondings; Metallic bonds; Ionic bond; Covalent bond; Hydrogen; Hydrogen halide; Acid–base reaction; Halogen; Oxygen; Redox reactions; Chemical equilibrium; Sulphur and Selenium; The nitrogen group; Nitrogen-Hydrogen compounds; Phosphorus; Arsenic, Antimony, Bismuth; Carbon; Germanium, Tin and Lead; Alkaline- earth metal; Alkali metal; Boron; Aluminium; Nobel gas; Ligand field theory; Catalysis

Introductory and Summary of Thermodynamics; State Functions; State Equation of an Ideal Gas; Force and Energy of Single Atoms and Molecules; The Degrees of Freedom of a Molecule and their Energetic Equilibrium; 1st Law of Thermodynamics – Work and Heat. What is a state function? State functions at constant pressure: Enthalpy, Real Gas – A System with Intermolecular Interactions; Entropy and the 2nd Law of Thermodynamics (Reversible – Irreversible Processes); Free Energy and Gibbs Free Enthalpy; The Gibbs Equation or fundamental thermodynamic relation; Multiple Component Systems – Equilibrium between Different Phases; Equilibrium of chemical reactions.

Digital Technology; Computer Architecture; Software Development; Variables and Elementary Data Types; Operators and Statements; Control Flow; Arrays, Strings, Pointers and Functions; Operating Systems; Higher Data Structures; Data, Databases; Modelling; Object Orientation and Object Oriented Modelling; Computer Communication

Principles of separation and identification of groups of ions; Preliminary tests and chemical dissolution; Extraction of solids; HCl/H₂S group; (NH₄)₂S group; CO₃^2--/soluble group/soda extract; Analyses of anions.

Basics of thermodynamics; thermodynamic systems; Variables of state; the thermodynamic equilibrium; introduction of temperature; thermodynamic state variables; First law of thermodynamics:first law for closed and open systems; enthalpy; caloric state variables and specific heat capacity; Second law of thermodynamics:reversible and irreversible changes of state; Exergy of open and closed systems; thermodynamic properties of matter; gas and vapour and there thermic and caloric state variables; Thermodynamic processes; Carnot cycle; Clausius-Rankine-Process

Advanced Mathematics 3: Orthogonal series, Fourier series, Hilbert space, multidimensional integrals, multiple integrals, surface integrals; differential equations, nonlinear differential equations, uniqueness, existence, stability.

Chemical equilibrium and titrations; Acid-Base Titration; Complexation Titration; Redox Titration; Gravimetric Analysis; Electrochemical Methods; Spectrochemical Methods; Chromatography; Thermal and Combustion analysis; X-Ray Methods; Mass Spectrometry.

Light and matter: First quantum mechanical introduction; NMR- and ESR-spectroscopy (nuclear and electron spin); Microwave spectroscopy (molecular rotation); Infrared and Raman spectroscopy (molecular vibrations); Instrumentation (spectrometer); Ultraviolet spectroscopy (excitation of electrons); Instrumentation (modern light sources: laser).

Structure and Bonds; Alkanes and Cycloalkanes; Alkenes; Alkynes; Stereochemistry; Alkyl halogenides; Alcohols; Ether; Carbonyl compounds; Carbonic acids; Aromats.

Statics; fundamental terms: properties of force and torque, operating experience and proceedings; systems of forces: plane and spatial; systems of forces, static equilibrium, equilibrium conditions graphical techniques: special cases of equilibrium, Culmann-line, link polygon method bearing statics: characteristics of bearings, bearing reactions; static determination; trusses centre of mass: weight, position of the centre of mass, moment and equilibrium, support of rigid bodies; beam statics internal forces and moments, FÖPPL-brackets kinetic friction: friction laws, application of friction laws, self-locking, belt friction rope statics

Fundamentals in momentum; heat and mass transfer; fluid mechanics; rheology; analogies in heat and mass transfer; unit operations

Flow-diagrams, design methodology, machine design, plant overview, basic stress analysis, failure modes, material properties, design fundamentals of vessel components at high pressure and temperature, fundamentals of FEM, fundamentals of fluid dynamics, valves, joints (welding, screws), flanged joints, leakage, national and international regulations

Thermodynamics and Kinetics -Stoichiometry and sequence of a chemical reaction, thermodynamic aspects of a chemical reaction, Basics in reaction kinetics, Basics in heterogeneous catalysis, micro kinetics in chemical reactions, Macro kinetics, Reaction vessels and process management -types of reactors, micro-/macro mixing and segregation, retention time analysis in ideal reactor types, modelling of real reactor systems, retention time and reaction, optimisation strategies for simple and complex reactions, heat management in reactors

Basic concepts of materials science including: material properties and solid state physics; atomic arrangements in solids; defects in crystals, polycrystals and their defects; solid state thermodynamics; phase diagrams, phase transformations; diffusion; strengthening mechanisms, heat treatment; chemical stability; additional material parameter

Elasto-Statics; stresses and strains: tension-compression-loading, state of stress, state of strain, relation between stress and strain; stability hypotheses; beam bending: moments of inertia of area, stress distribution in a beam, deflection curve, influence of shearing stresses, principle of superposition; torsion: circular cross section, thin-walled cross section buckling: buckling equations and their solutions, Euler’s buckling load, computation of compression struts; energy methods: Castiglione’s method, principle of Menabrea, strain energy; principle of virtual work

Introductions – Mechanisms of heat transport; basic term of heat transfer, Fourier law and differential equations, boundary conditions; stationary heat transfer; Péclet-equation for plate, cylinder and sphere; 2D- heat transfer, heat transfer with constant source; Biot- and Fourier-number; Introduction to heat radiation: emission and absorption of black and non-black bodies Kirchhoff’s Law; optical Properties, Radiation and heat transfer; Mass and Energy balance; heat exchanger; fundamentals of heat transfer and convection, basic result of fluid mechanics, differential equations for temperature and heat transfer in fluids; Nußelt-Number; Pi-theorem; free convection; Boussinesq-approximation

Chemical Reactivity; Classification of Organic Reactions; Reactive intermediate stages and Acid/Base Chemistry; Nucleophilic Substitution; Elimination Reaction; Addition Reaction; Cycloaddition Reaction; Aromatic Substitution; Radical Reaction; Oxidation and Redox Chemistry; Reaction of Carbonyl Compounds; 1, 2 Addition Reaction of Organometallic Compounds; Enolates; Rearrangement Reaction.

Measurement of effective diffusion coefficients; Macro kinetics of the gas-liquid transition in chemical multi-phase-reactions; Transport limitation in the catalysis with split catalisis; Adsorption; Retention time and chemical reactions (pipe, cascade, stirrer); Stability characteristics of a continuous enhanced stirred-tank reactor

Introduction into processes of Mechanical Process Engineering, particles and disperse systems, particle collectives, particle analysis techniques, separation technology, mixing of particles, Dimensional analysis.

The aim of this course is to teach the engineering and thermodynamically basics of thermal separation processes. Main focus will be:Thermodynamic of single component systems and mixtures with are detailed view on the equilibrium state.(chemical equilibrium and phase equilibrium)calculation of gas-liquid-equilibriumstate diagrams of ideal and non-ideal gases and mixtures distillation processes (open and closed)rectification processes (binary mixtures) tray columns and packed columns

Chemistry of water; biophysics (structure of cells, biological membranes and mass transfer, biopolymers); biochemical energetics (catabolism, anabolism, substrate phosphorylation, respiration, thermodynamics); genetics (genes, gene expression, recombinant DNA-technology); enzymes (classification, kinetics, technical applications, immobilisation); cells (growth, kinetics, reactors, technical applications); sterilisation (methods, kinetics, heat transfer, aseptic design); downstream-processing of bio products (cell separation, cell disruption, extraction/ adsorption, chromatography); bio analytics

1. Control technology 2. Phase equilibrium 3. Two-material rectification 4. Tube bundle heat exchanger 5. Retention time 6. Liquid-liquid extraction 7. natural circulation evaporator 8. Fluid dynamic of a plate/ packed column 9. Gas absorption 10. Adsorption

Physics of fluids; kinematics of flows; conservation laws of fluid mechanics; Bernoulli equation; wave phenomena and gas dynamics; viscous flows; turbulence; technical flows

Research Project in the field of Chemical Engineering or related topics, conducted at the Technical University of Munich (TUM) in Munich, Germany

Fundamentals: 1. real and complex numbers, supremum, induction, notion of functions, mathematical notation. 2. Sequences, series, limits, continuity.3. Integral and differential calculus.

Vectors, matrices, linear equation systems, scalar and vector product, determinants, orthogonality, linear spaces, linear transformation, eigenvalues, matrix factorizations (especially diagonalization and singular value decomposition), matrix norm, Linear differential equations with constant coefficients.

1. Basics of digital information representation, informationprocessing and storage: number representation and arithmetic operations inbinary number system.2. Basic model for functional behaviour of MOSFET transistors, current equation, delay and dynamic power. 3. Circuitry-wise realization of arithmetic operations (addition, subtraction, multiplication) as well as the synthesis of bi- and multiple-stage combinatorial operations (conjunction, disjunction, negation) and sequential switchgears consisting of basic components (logic gates, registers, MOSFET transistors). 4. Logic optimization of combinational circuits (switching network). Techniques to improve the information flow of clocked, sequential switchgears via pipelineand parallel processing. 5. Role and structure of finite state machines as control and monitoring units of multiple convenient applications. 6. Basics of methodological testing of circuits: faultdiagnosis, derivation of fault coverage tables, testing regulations in combinational circuits and sequential switch gears. 7. Besides the functional aspects of digital circuit technologyandthe causes and limits of performance, the time response and the energy consumption of digital complementary metal oxide semiconductors (CMOS) technologies in the context of information and communication technology (ICT) are taught. 8. In addition necessary economic aspects of CMOS are addressed.

Linear and nonlinear resistive circuits.1. Lumped-Circuit Approximation, Modelling: Electric devices, circuit elements, graphs, Kirchhoff’s laws, linearity. 2. One-ports: v-i characteristics and properties, parallel and series connections, DC-operating point and linear approximation, small-signal analysis. 3. Two-ports: Representations and properties, vector space approach, special two-ports, connections. 4. Transistors: Modelling of bipolar and field-effect transistors, basic circuits and their analysis (DC-points and small-signal approximation). 5. Operational Amplifiers: Linear and nonlinear modelling, basic circuits. 6. Multi-ports: Representations und special multi-ports. 7. Circuit Analysis: Interconnect and its properties, Tellegen’s theorem, incidence matrices, tableau analysis, node and loop analysis, direct set-up of the node-admittance matrix. 8. General Circuit Properties: Substitution theorem, superposition theorem, Mayer-Norton and Helmholtz-Thevenin theorems, passivity, incremental passivity und monotonicity. 9. Logic Circuits: Boolean algebra, basic gates and their realization.

Mechanics, oscillations and waves, thermodynamics, optics, atomic and nuclear physics

1. Integral and differential calculus (multidimensional): curves, scalar and vector fields, partial derivative, gradient, total derivative, functional matrix, implicit functions, extreme values with and without constraints. 2. Differential and integral calculus (multidimensional): vector fields, line integrals, potential, and volume integrals. 3. Differential equations: ordinary differential equations, special types of 1st order differential equations.

Automata theory, formal languages and grammar, fundamental string processing, design and analysis of algorithms, abstract data structures, graphs, trees, lists, pointers, queues, stacks, basic algorithms, sorting, searching, graph algorithms, complexity measures, modelling, basic programming techniques (loops, branches, pointers, etc.), basic language structure (programming using C), usage of editors and compilers.

Structure of computer systems, micro-architecture, instruction set architecture, data and instruction formats, assembler programming and high-level language, interaction of computer programs and operating system, operating system tasks.

Linear and nonlinear dynamic circuits.1. Energy Storing Elements: Nonlinear and linear capacitor and inductor, curves in the u-q- and i-phi-plane, duality of charge and flux. 2. Properties of dynamic one port: linearity, memory and initial state, continuity, lossless property, energy storage and relaxation points. Series and parallel connection of dynamic one ports.3. Dynamic multi ports.4. First Order Circuits: Linear and piece-wise linear resistive circuits connected with a linear dynamic one port. Calculation of the port variables of time invariant circuits for constant, piece-wise constant and arbitrary excitations.Time variant circuits with switches. Piece-wise linear first order circuits: dynamic route, equilibrium states, impasse point, and jump phenomenon. Relaxation oscillators and bistable circuits. 5. Linear Second Order Circuits: System of coupled first order state equations in two state variables. Equation formulation, realization of the state equation. Zero input case: solution of the state equation with the eigenvalues and eigenvectors of the A matrix and transformation to the normal form. Discussion of solution types and types of equilibrium states with phase portraits and time functions. Consideration of autonomous systems and systems with arbitrary excitations.6. Nonlinear Second Order Circuits: Nonlinear resistive two ports connected with two linear dynamic one ports. Piece-wise linear two ports: classification of equilibrium states and sketch of phase portrait. Constant-energy circuits. 7. Limiting orbits: linear oscillator, relaxation oscillator. 8. Phasor Analysis: Systems with sinusoidal excitation in steady state. Properties of phasors: uniqueness, linearity, and differential rule. 9. Network functions: complex frequency and natural frequencies, frequency response: Bode plots.

Physical theory of electric and magnetic phenomena, that is relevant to technical applications:
1. Electrostatics: charge, electrical field, potential, capacity, electrical energy. 2. DC: current density, charge conservation, Kirchhoff’s circuit laws, Ohm’s law. 3. Magneto statics: magnetic fields, solenoidal fields, Ampere’s law. 4. Magnet. 5. Induction: electromagnetic induction (motional and motionless induction), inductivity, magnetic energy. 6. AC: linear circuit elements, complex AC analysis

1. Orthogonal series (especially Fourier series), Fourier transform, Hilbert space. 2. Partial Differential equations. 3. Complex analysis: Properties of analytic functions and integral transforms, residue theorem, Laurent expansion (Laurent series), singularities. 4. Differential equations: continuation of linear theory, nonlinear differential equations, existence and uniqueness theorems, stability.

Time-continuous and time-discrete signals, linear time-invariant systems (LTI-systems), convolution, convolution integral and convolution sum, pulse response of LTI-systems, stability and causality, periodic signals, orthogonal function systems, time-continuous Fourier series (FS), time-continuous Fourier transform (FT), Fourier integral, relationship between FS and FT, corresponding TF pairs, amplitude modulation and signal reconstruction, linear differential equations and transfer functions, Bode diagram, introduction to filter technology, time-discrete Fourier transform (TDFT), linear differential equations, time-discrete filters, sampling in the frequency domain, Laplace transform (LT), convergence properties of the LT, z-transform, residue theorem, discrete Fourier transform (DFT).

1. Probability theory: sample space, sigma algebra, probability measure, conditional probability, stochasticindependence, Bayes’ theorem, discrete and real random variables, probability distribution and density, joint distribution and density, functions of random variables, expectation and variance, conditional expectation, generating and characteristic function, central limit theorem, law of large numbers and Chebyshev inequality. 2. Standard stochastic models: (Bernoulli) uniform, binomial, Poisson, geometric,normal and exponential distribution. 3. Stochastic random sequences: ensemble of random variables vs. Path model, distributions and densities of random sequences, discrete random walk process, convergence of random sequences, Markov property, Markov chains. 4. Random processes: auto- and cross-correlation function, Wiener-Levy process, Poisson process, Markov processes, classification of random processes, power spectral density, Wiener-Khintchinetheorem, linear systems and random process, white Gaussian noise, deviation and integration of stochastic paths, the MSE-calculus and the Karhunen-Loeve development of random processes.

Theory of electromagnetism from field theory point of view as basis for the physical understanding of electromagnetic phenomena in technical applications:
1. Maxwell equations, material models, energy transport and electromechanical forces. 2. Electromagnetic waves: polarization, dispersion, damping, reflection, refraction. 3. Radiation of antennas in free space. 4. Reciprocity theorem.

Basics of quantum mechanics; structure of matter (atoms, molecules, crystals); mechanical, thermal, dielectric, optical and magnetic properties of solids; electrical and thermal transport, free electron gas; metals, dielectrics, plastics, glass and ceramics; energy band model; semiconductors and their applications; superconductivity; the most important materials for applications in electronics

Numerical Analysis and Optimization: linear and nonlinear equation systems, error analysis, interpolation, numerical integration, initial value problems for ordinary differential equations (ODE), boundary value problems, partial differential equations.

1. Propositional Logic: propositional forms, truth-set, laws of propositional logic, rules of inference; law of resolution; logic conclusions; binary decision diagrams (BDDs), operations on BDDs (application: e.g. logic verification, logic synthesis). 2. Predicate Logic: predicate logic forms, laws of predicate logic, deduction scheme, induction (application: e.g. petri nets). 3. Sets: notation, operation, relations between sets; Boolean algebra of subsets (application: e.g. string operations, discrete system simulation). 4. Relations and Graphs: fundamentals, operations on relations; properties of relations, representation of relations (e.g. matrix representation); closures, order relations, equivalence relations (application: e.g. graph algorithms); binary graphs, possibly graph algorithms; extrema. 5. Finite State Machines FSMs (possibly very briefly, depending on contents of other lectures): relation-based description; optimization of FSMs. 6. Algebraic Structures: rings: fundamentals, properties, substructures, homomorphism and isomorphism, modular arithmetic; groups: fundamentals, properties, homomorphism and isomorphism, coset. 7. Complexity Theory: numbering, elementary counting; asymptotic behaviour of cost functions.

Source signals and their spectra.Sampling theorem, quantization, basic concepts of the rate-distortion theory, pulsecodemodulation (PCM), differential PCM. Basic concepts of information theory, source coding, entropy encoding. Baseband transmission: pulse waveformsand their spectra, Nyquist criterions, eye diagram. Transmission channel (e.g. AWGN-channel), matched filter, detection in random noise, error probability for anti-periodic and orthogonal transmission, linear digital modulation schemes (PSK, QAM), realization aspects (clock, phase and frequency estimation).

Basics of open-loop and closed-loop control, automation in technical and nontechnical systems. -Modelling, linearization and linear systems. – Time response of linear dynamical systems. –Standard dynamic system components, time-lagged systems. – Stability of LTI-systems, stability criteria. – Basicsofclosed- loop control and standard controllers. – Stability analysis of closed-loop control circuitsin the frequency domain, Nyquist- and Bode-diagrams. –Control unit design and methods for controller parameters. – Structural extension of single closed loop control structures via feed forward control and controller cascades. – Condition-based control unit design, linear-quadratic control, state monitor of LTI-systems. – Digital implementation of open-loop control, closed-loop control regulations and filter laws. – Discrete event open-loop control and Petri-Netz-modelling, coordination of partial control. – Technology of regulatory, control (open-loop control and closed-loop control) and automation systems. – Application examples.

Introduction to digital measurement systems, measuring amplifiers and bridges, display, conversionand processing of measurement data, measurement systems with resistive, capacitive and inductive sensors, technical temperature measurement, measurement systems with optical sensors, electric and magnetic effects in sensor materials, measurement systems with ion-conducting sensors, measurement systems with gravimetric sensors, measurement systems with time delay and Doppler sensors.

Importance of electricity industry, generation of electrical energy, energy storage technologies, three-phase system (alternating current technology), electric machines, transmission of electrical energy, electric power grids, high voltage technology, electric drives, (electronic) power converters, electrical safety.

1. Basics in semiconductor electronics: bonding model and energy band structure, Electrical and optical properties of semiconductors, carrier transport, PN-junction and filed effect. 2. Structure and operation of semiconductor devices: Diodes (PN diodes, Schottky diodes, and optical diodes), bipolar transistor, MOS structure and field effect transistor, memory cells, IGBT, thyristor.

1. The lecture serves as an introduction to cryptology and IT-Security,starting with the basic aspects of security: confidentiality, authenticity and integrity, anonymity, non-repudiation, authorisation and access control as well as threats and risks in IT-Security. 2. The relevant results from discrete math are reviewed with special focus on the arithmetics of finite fields and elliptic curves. 3. The discussion of cryptographic mechanisms (symmetric vs. asymmetric cryptography, stream cyphers, hybrid cryptography, one-way- and hash-functions, digital signatures) is succeeded by the inspection of important cryptographic algorithms. Common primitives are considered along with their modes of operation. 4. The application of these algorithms for cryptographic protocols such as challenge-response procedures, Diffie-Hellman key exchange, the Fiat-Shamir protocol, Kerberos and public key infrastructures is covered. 5. Complementary the implementation of complex secure systems such as PKI-infrastructures and access control will be studied as application examples. 6. Finally the design of secure systems, “system engineering” is discussed.

1. Transfer function and impulse shaping 2. Time-continuous circuits and systems: 2.1 State space representation: forms of realization (direct form, normal form, and cascade form), sensitiveness. 2.2 Standard approximations: Butterworth-, Tschebyscheff-, Cauer- und Bessel-filter. 3. time-discrete circuits and systems: 3.1 Transfer functions of time discrete systems. 3.2 FIR- and IIR-systems, 3.3 FIR-filter design: linear phase FIR-filter, window function, LS-design in the frequency domain, minimum phase FIR-Filter. 3.4 IIR-filter design: Richards transform, Bilinear transform, time-discrete integrators. 3.5 Frequency transformations. 4. Stability: 4.1 Observability and controllability, 4.2 stability of state, bibo stability. 5. aadaptive signal processing: 5.1 Channel estimation: correlator, LS-estimation 5.2 Unbiased filtering: Zero- Forcing Algorithm, 5.3 Signal adapted Filtering: Matched Filter, comparison between Zero-Forcing Filter and Matched Filter; 5.4 Wiener-Kolmogorov Filtering: least square method, minimum mean-square error by Wiener Filter, comparison with Zero-Forcing and Matched Filter

This course gives students the opportunity to learn the basics of the design and the characterization of analog circuits. Therefore basic circuitry (e.g. differential pair, current and voltage references) has to be designed with standard industry-tools (Cadence, Matlab). The students have to develop the full schematic diagram and dimension the device parameters. Afterwards the circuitry has to be assembled with discrete devices and the functionality has to be tested. The device and circuit parameters have to be determined and evaluated with test circuits and measurement equipment. Familiarization with CAD environment, PVT (Process, Voltage, and Temperature) variation, Transistor Characterization.

The aim of the module is to provide the students with knowledge and understanding of practical Integrated Circuit (IC) design techniques in digital IC. It includes both digital IC design at transistor level as well as system level using hardware description language (HDL). Verilog-HDL is the targeted HDL in this semester. This is a full laboratory course with 100% laboratory assessment, and that’s no written examination.

Understanding of micro-structured energy converter system design and dimensioning of micro-transducers, piezoresistive transducers, piezoelectric transducers, magnetic transducers, Calculation of basic structures and design of micro-structured mechanical and fluidic elements

The Lecture “Real-Time and Embedded Systems” covers the topics:
1. Basics of embedded processor architectures 2. Bus and memory architectures 3.Performance/Timing analysis of embedded systems 4.Models for real-time systems 5.Principles of embedded software development, 6.Basic real-time programming language concepts (e.g. Esterel) 7.Real-time operating systems 8.Power management 9.Design space exploration

Representation and Analysis of Multi-Input Multi-Output Systems, performance specification and limitations, H control (PK structure, H control problem, Mixed sensitivity design, characterization of H norm, control synthesis), bisection algorithm.

The laboratory consists of experiments on the following topics: computer aided control design, state space control design, systems with distributed parameters, machine vision in automation systems, mobile robots, automation with petrinets and neuronal networks.