Compulsory Modules, Semester 1 and 2

Mechanics:

• Kinematics and dynamics of mass points
• Dynamics of point systems and rigid bodies
• Mechanics of gases and fluids

Thermodynamics:

• Terms, equations of state
• Elements of kinetic gas theory
• First and second law of thermodynamics
• Application of the laws

Electricity and Magnetism:

• Electrostatics, stationary currents
• Magnetic fields, time variable currents
• Maxwell equations

Wave theory:

• Wave dispersion (elastic and electromagnetic waves)
• Breaking, bending and interference in acoustics and optics

Further topics:

• Mathematical tools (vector fields, complex notation)
• Additional lecture experiments for Physics I & II
• Additional topics for Physics I & II (e.g. tops, hydrodynamics)
• Theory of special relativity
• Maxwell equations in differential form
• Radiation of illuminated charges (e.g. dipole or synchrotron radiation)

Selected experiments, including writing of a report and completion of an error calculation:

• Measurement of physical quantities and error calculation
• Absorption of radiation and radioactivity
• Determining of mechanical quantities and material constants
• Mechanical oscillations and resonance
• Steam pressure curve of water
• Specific warmth and adiabatic index
• Determining of fundamental constants
• Alternating current circuits
• Magnetic field measurements
• Waves and interference, optical representation
• Spectroscopy

• Taylor Expansion

• Differential equations

• Vector fields

• Differential operators, gradient, divergence, rotation

• Complex notation

• Matrix inversion, Eigenwerte

• Fourier Transformations

• Hydrodynamics, Navier-Stokes equations

• Gravity, Kepler's Law

• Atmospheric Physics

• Brownian motion and transport phenomena

• Fourier optics and wave theory

• movement of charges in el-magn. fields

• Linux
• Graphical Display
• Programming in Python
• Important algorithms and program libraries for linear algebra, differential equations and probability/statistics
• Various examples in Physics

• Differential and integral calculus for real value functions with one variable
• Number systems: Completion from Q to R; complex numbers
• Sequences and series; Constancy of functions; Sequences and series of functions; Intermediate value theorems
• Differential calculus; local behavior of functions (Extrema); Mean value theorems; Riemann integration; Fundamental theorem; Improper integrals
• Elementary functions
• Power series and Taylor series, multivariate differential calculations
• Derivatives of multivariate graphs; partial derivatives, Taylor series; local behavior of a graph;convexity
• Theorem of inverse functions; theorem of implicit functions; real manifold; local extrema with constraints
• Integral calculations in Rn; transformation equation; length and area content
• Vector analysis: vector fields, rotations, divergence, Stokes’ theorem; divergence theorem; Green’s theorem

• Basics and algebraic structures: sets, groups, bodies, rings, Euclidean rings, residue bodies and body extensions
• Matrices and linear systems of equations:vector spaces, matrices, Gaussian elimination method, linear dependence, generating system, basis, equivalence of matrices, similarity of matrices, linear algebra over rings
• Determinant: Symmetric group, Multilinear mappings, Determinant as normalized alternating mapping, Further properties of the determinant, Orientation
• Eigenvalues and eigenvectors: Definition and diagonalizability criterion, characteristic polynomial and trigonalizability, theorem of Cayley-Hamilton, fundamental theorems

• Tensors
• Infinitely dimensional vector spaces

The Guide to Physics Studies provides comprehensive information about the Bachelor's and Master's programs.