Curriculum in Mathematics Pre-semester


Physics                              Chemistry                                Mathematics


Course Curriculum

Part I: Calculus


1) Basic concepts

Sets; set relations and operations.

2) Functions

Real-valued functions of one variable; graph of function; continuity;
polynomials; rational functions; algebraic functions; natural exponential
function; trigonometric functions; natural logarithmic function.

3) Differential calculus

First derivative; tangent; linear approximation; differential; product rule;
quotient rule; chain rule.

4) Limits

Definition; evaluation

5) de L’Hôpital’s rule

Criteria for application.

6) Integral calculus

Definite integrals; fundamental theorem of calculus; indefinite integrals;
integration by parts; substitution method; partial fractions
decomposition of rational functions.

Part II: Vector algebra


1) Basic concepts

Column vectors; row vectors; addition and scaling of vectors; linear
in-/dependence of vectors; vector basis.

2) Linear systems

Gaussian elimination; matrices; addition and scaling of matrices; matrix
product; linear maps.

3) Scalar product

Orthogonality of vectors; length of vector; normalisation; angle
subtended by two vectors; representations of planes in 3-D Euclidian

4) Decomposition of vectors

Components of vector with respect to given basis; projection of vector
onto other vectors.

5) Determinants

Area of parallelogram; volume of parallelepiped.

6) Vector product

Definition; properties; applications.


Physics                              Chemistry                                Mathematics


Curriculum in Chemistry Pre-semester


Physics                              Chemistry                                Mathematics


Course Curriculum

1) Atoms, Elements and the Periodic Table

  • Elementary particles
  • Elements
  • Electron shells and the periodic table
  • Chemical Formulae and stoichiometry
  • Avogadro’s constant and the mole

2) Covalent Bonding

  • The octet rule
  • Lewis (valence-bond) formulae
  • Simple reactions
  • Reaction enthalpie

3) Ionic Bonding

  • Formation of ions
  • Crystal lattices
  • Lattice energies
  • Bosch-Haber cycles

4) Bonding in Metals

  • Structures of metals
  • Hard and soft metals

5) Solutions

  • Concentration
  • Water as solvent
  • Salvation of ions and covalent compounds
  • Entropy and free enthalpy of solution
  • Dependence of solubility on temperature and pressure

6) Equilibria

  • Mass-action law and equilibrium constants
  • Position of equilibrium
  • Metastable systems
  • Catalysts
  • Solubility product

7) Acids and Bases

  • Br?nsted an Lewis theories
  • pH and ionic product of water
  • pKa and acid strength
  • calculation of pH in aqueous solutions
  • pH of basic solutions and pKb
  • proton transfer in solutions of metal salts and amphotericity
  • buffer solutions and indicators
  • Lewis acids and bases

8) Redox Reactions

  • Oxidation states
  • Oxidation and reduction
  • Redox equations
  • Electrochemical series

9) Electrochemistry

  • Electrolysis
  • Galvanic cells
  • Standard potentials
  • The hydrogen electrode
  • The Nernst-equation
  • Decomposition voltage and overvoltage
  • The lead accumulator
  • Local cell and corrosion

10) Selected Topics in Chemistry (topics to choose from)

  • Synthesis of Ammonia
  • Blast Furnace process and Steel production
  • Aluminium production
  • Production of sulphuric acid
  • Chemistry of metals
  • Chemistry of non-metals
  • Salts

11) Organic chemistry

  • Alcanes, Alcenes, Alcines
  • Alcohol
  • Carbonic acids
  • Ester
  • Synthetics and plastics


Physics                              Chemistry                                Mathematics


Curriculum in Physics Pre-semester


Physics                              Chemistry                                Mathematics


Course Curriculum

The duration of the written exam is 3 hours. The only aid allowed is a non-programmable calculator.

The exam covers the following:

1. Basic concepts

Introduction to the methods used in physics, basic physical measures, the International System of
Units and derived units

2. Statics

  • Forces (composition and decomposition of forces)
  • Hooke’s law, simple machines
  • Torque, equilibrium of a rigid body, centre of gravity

3. Kinematics and kinetics

  • Uniform motion and linear motion with constant acceleration, principle of superposition, composition of motion,
  • Newton’s laws, friction, work, energy, power, impact, momentum
  • Conservation of energy and momentum, applications (collisions)
  • Circular motion, planetary motion, gravity, work in the gravitational field, verification and effect of the rotation of the earth, rotation of a rigid body: Moment of Inertia, rotational energy, angular momentum, conservation laws, simple rotation problems, independent axis.

4. Oscillations and waves

  • Harmonic motion, the mathematical and physical pendulum, rotating pendulum, enforced oscillations and natural oscillation,
  • Wave motion, superposition and reflection of waves, the Doppler effect, the Huygen effect

5. Basics of magnetism

Permanent magnet, magnetic dipole, magnetic induction, magnetic field of the earth

6. Electric charge, electric induction

  • Coulomb’s law, electric fields (especially homogeneous and radial fields), electric field strength, work in an electric field, electric potential, voltage, parallel plate capacitor, cylindrical capacitor, capacity,
  • electric charge in uniform motion, matter in an electric field, energy of the electric field, energy
  • density.

7. Electric direct current

Effects of electric current, amperage, voltage, resistance, conduction mechanisms in solid and fluid bodies, in gases and vacuum (electron tube and semi-conductors), Ohm’s law, Kirchhoff’s rules, electric meters, electric work and power

8. Electromagnetism

Magnetic field of a coil, magnetic flux density, magnetic flux, induction law, magnetic induction, self inductance, matter in the magnetic field, Lorenz force, energy of the magnetic field, energy density, electromagnetic machines (electric motor, generator, electric magnet) transformer

9. Electric oscillations and electric waves

Coils, condensers and resistance according to Ohm in d.c. voltage and a.c. voltage, closing and opening of a circuit, electric resonant circuit, rms-value, Ohm’s resistance, inductive resistance and capacitative resistance, impedance, effective power, diode, triode, transistor, broadcasting, reception and propagation of electric waves


Physics                              Chemistry                                Mathematics


The Bachelor Program in Mechanical Engineering at Carl Benz School of Engineering. Germany

Like other Bachelor’s programs around the world, this one takes about four years (eight semesters), with graduation following the completion of a final written thesis. But unlike other programs the English-taught engineering courses offered are complemented by a series of German-taught interdisciplinary classes which include business administration and cultural issues. Additionally, multiple industrial internships are mandatory and an integral part of the program.

Preview of Syllabus – Bachelor of Science in Mechanical Engineering

In the first term or pre-semester (beginning in August prior to the winter semester) students take a set of science classes and tutorials designed to bring them up to the same level of necessary scientific background  corresponding to the German “Abitur” as well as to improve (if necessary) their English language skills. Intensive English and German classes are offered during the pre-semester. At the same time students are introduced to the basics of computer based study and work-techniques as well as to computer-based tools for “Office Applications”.

After this pre-semester, freshmen take written exams in English, Mathematics, Chemistry and Physics. The results of these examinations qualify as a cumulative entrance exam. The next 4 semesters of major courses cover the same material in mechanical engineering as the German-language “Vordiplom-Program” offered by the University. The next milestone to be  encountered is that all advanced mathematics I-II exams and all engineering mechanics I-II exams have to be passed for the students at the end of the 4th semester  in order to continue their studies.

The bachelor intermediate- diploma is equivalent to the german “Vordiplom” and should be accomplished within 6 semesters. The 6th to 8th semesters encompass English language lectures on selected topics of mechanical engineering, e.g. Fluid Mechanics, Systems and Control Engineering, Integrated Product Development and Industrial Plant Management. After the completion of the lecture curriculum the students have to write a bachelor thesis.

Furthermore, during spring and summer breaks between semesters, students are expected to successfully complete at least 16 weeks of industrial internships for the Bachelor Degree. If students want to continue their academic education with a Masters Degree they are able to choose from a variety of specialization topics offered at the mechanical engineering department.  But please note that some of these specialization topics will only be available in German. For a Master’s Degree 26 weeks of internship are required.

Of immediate concern for new entrants in the Carl Benz School is to successfully clear the pre-semester examination in October following which one actually qualifies to proceed further. Please check on the following links to see the relevant course curriculum during this short pre-semester period.

Pre-semester Physics Pre-semester Chemistry Pre-semester Mathematics

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