# Requirements

Here the requirements with regard to the content of the study course are given.

All requirements regarding to formal aspects of your application are listed in the topic
“Application”.

The master course in Materials Science and Engineering requires a bachelor degree in a
field of natural sciences or techniques.

The following keywords must be known in basics
for theory and practice.

Here you
can print out a check list.

### Materials Science

- models of atoms, Schrödinger equation and principles of quantum theory, bonding, concept of potential wells
- perfect crystals: formal description, important lattices
- real crystals: defects in crystals, types of defects, interaction of defects
- thermodynamic equilibrium: types of equilibrium, 1st and 2nd law of thermodynamics, statistical interpretation of the entropy, applications to point defects
- kinetics: reaction rates and Boltzmann factor, phenomenological diffusion and atomic mechanisms
- mechanical properties I: stress and strain, phenomenological description of deformation, brittle behavior and fracture
- mechanical properties II: mechanisms of plastic deformation, dislocation movement and multiplication, theory of yield strength
- structural and mechanical properties of amorphous materials and polymers
- general structural properties, modulus of elasticity, viscose and inelastic behavior, deformation and fracture
- aging and failure of materials: mechanisms in general, fatigue and creep, corrosion, electromigration and special mechanisms
- electronic properties in general, electronic properties and materials science.
- electrons in crystals: classical theory, Hall effect, quantum description, free electron gas model, density of states, Fermi distribution and Fermi energy, properties of the free electron gas
- diffraction in crystals: basic consideration of diffraction in crystals, Bragg law, reciprocal lattice and Ewald construction, intensity of the diffracted waves
- electrons in a periodic potential: Free electron gas plus Bragg law, Brillouin construction of diffraction, band structures and electronic properties, band-band transitions and standard representation of semiconductor band structures
- semiconductors: intrinsic conductivity, conductivity as a function of temperature, the concept of holes, doping and extrinsic conductivity
- semiconductor contacts: surface states, space charge region, p-n-junction, currents and current-voltage characteristics, recombination and diffusion current

### Mathematics

#### Calculus

- real and complex numbers, complete induction, sets, functions. Series of real numbers, convergence, Cauchy series
- steadiness, theorems on continuous functions, polynoms, nulls, rational functions
- inverse functions: exponential functions and logarithms, trigonometric functions, hyperbola functions
- differential calculus: characteristics of differentiable functions and differentiation rules, derivatives of basic functions, median theorem, extrema, Taylor’s and L 'Hospital’s rules
- integral calculus: antiderivative, indefinite integrals, substitutional rules, partial integration, factoring of polynomials, Riemann integrals, examples of continuous and monoton functions, main clause of differential and integral calculus.
- indefinite integrals: gamma function, Stirling’s formula
- infinite series: criterions on convergence, power series, monotonous convergence, differentiation and integration of individual terms, examples on Taylor series, criteria of convergence with respect to Fourier series
- arc length, curvature, convergence criteria; power series, uniform convergence, differentiation and integration by segments, examples for Taylor series
- Fourier series: questions of convergence, Bessel's inequality
- Taylor's formula
- extrema of functions in several variables, least squares method, Lagrange multipliers
- integration
in R
_{n}: integral over domains, iterated integrals (Fubini), volume, substitution rule: polar and spherical coordinates

#### Algebra

- Euclidean vector spaces in R2, R3: vectors, scalar product, matrices, linear maps in R2, vector product in R3
- analytic geometry in R2, R3 vector spaces: linear independence, basis, dimension, linear maps and matrices, rank
- linear systems of equations: solvability, Gauss' algorithm, L-R-factorization, inverse matrix, Cramer's rule
- Eigenvalues and eigenvectors, characteristic polynomial, scalar product and norm, Schwarz inequality
- Legendre polynomials, orthogonal and unitary maps
- linear transformations: eigenvalues and eigenvectors of symmetric and orthogonal matrices, quadratic forms
- some
topology in R
_{n}: open, closed, tangent plane, directional derivative, special partial derivatives, gradient, direction of maximum slope

### Chemistry

#### Inorganic Chemistry

- periodic
system of elements, names, periodic properties, electron configuration
- usage of the elements and their compounds
- atomic
structure, crystals, amorphous materials
- chemical
bond types, covalent, ionic, metallic, van-der-Waals
- reactivity of chemical element, redox potential, oxidation, reduction
- simple inorganic synthesis
- acids
and bases, strength, order
- pH
value, neutralization, titration
- chemical equilibrium
- indicators
- basic chemical analysis

#### Organic Chemistry

- alkane, alkene, alkyne
- alcohols, ketones, aldehydes, acids
- cyclic molecules, hetero structures, amoatics
- nucleophile, electrophile substitution and addition
- common reactions
- polymerisation, reactions, modes, usage
- nomenclature
- basics
of stereo chemistry, chirality, stereo selectivity
- basics of natural products chemistry

#### Physical Chemistry

- ideal and real gases
- fundamentals of the kinetic theory of gases
- thermodynamic state variables
- laws of thermodynamics
- chemical transformations
- thermochemistry
- phase transition and equilibrium
- multicomponent systems
- phase diagrams
- chemical equilibrium
- fundamentals of equilibrium electrochemistry

### Physics

- Fundamentals of physics with a special emphasise on classical mechanics, electricity, optics and acoustics
- Introduction into physics of atoms, molecules, nuclei, elementary particles
- Basics of solid state physics