3.1 Recapitulation: Derivatives and Integrals
3.2 Calculation rules for derivatives
3.2.1 Prove of product rule and chain rule
3.3 Calculation rules for integrals
3.4 Sequences and Series
3.4.1 Examples: Convergence of infinite series
3.5 Taylor series and their application
3.5.1 Example: Taylor expansion of exponential function
3.5.2 Example: Taylor expansion of sin function
3.5.3 Example: Taylor expansion of cos function
3.5.4 Example: Taylor expansion of the logarithm function
3.6 Taylor series and error estimation
3.6.1 Example: Transformation of a non linear problem into a linear problem
3.6.2 Example: Taylor series of arctan function and pi-calculation
3.7 Linear Optimization
3.8 Fitting to an orthonormal set of functions
3.9 Functions as vectors
3.10 Schmidts orthonormalization procedure
3.11 Fourier series
3.11.1 Example: Periodic step function
3.11.2 Example: Positive part of sin function
3.11.3 Example: Absolute of sin function
3.11.4 Example: Periodic parabolic function
3.12 Fourier series in complex description
3.12.1 Example: Fourier-Series with larger periodicity length
3.13 From Fourier series to Fourier-Transformation
3.14 Fourier-Transformation: Definition
3.14.1 Examples for Fourier transformation
3.15 Fourier Transformation: Properties
3.15.1 Convolution Theorem: Proof and example
3.16 Fourier Transformation: Solving DEQs
3.16.1 Forced oscillations: 2. Example for solving DEQ with Fourier Transformation
3.17 Important non-elementary functions: Gamma function
3.18 Important non-elementary functions: Delta function
3.19 Important non-elementary functions: Gauss- and Error function
3.20 Aspects of probability theory
3.21 Aspects of noise analysis