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; CO32--/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.

Enzymes (biochemistry, kinetics, thermodynamics, immobilized enzymes, industrial use of enzymes) Bioreactors (functionality, process parameter, sensors, design of bioreactors and bioprocesses) Growth kinetics and mass balancing (calculations for batch, fed-batch, and continuous batch fermentation, material balancing) Heat and mass transer (heat exchange, conduction, convection, oxygen uptake rate, diffusion, combined mass-transfer coefficient) Industrial microbial bioprocesses (production of food, biomass, alcohols, organic acids, antibiotics) Downstream processing (cell disruption, filtration, chromatography, centrifugation, extraction, drying) Sterilization processes (physical and chemical methods, practical rules working with microorganisms) Analytics for process control(GC, HPLC, spectrometry, bioanalytics)

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

*This module outline is only applicable to Polytechnic graduates with exemption credits.