In this way, they have the ability to integrate their knowledge into new problems and to deal with complexity. They also can apply their knowledges and problem solving skills in new, unfamiliar multidisciplinary situations.

1. Raumkurven, Vektorielle Parameterdarstellung, Tangentenvektor, Krümmung
2. Skalar- und Vektorfelder, Gradient, Divergenz, Rotation, Niveaulinien, Richtungsableitung, Quellenfreiheit, Wirbelfreiheit, Laplace-Operator, Laplace-Gleichung, Poisson-Gleichung
3. Kurvenintegrale, Potenzialfunktion, konservative Felder
4. Kombinatorik, Wahrscheinlichkeit, Permutation, Kombination, Variation, De Morganschen Regeln, Zufallszahlen, Histogramm, Wahrscheinlichkeitsdiagramm
5. Verteilungen, Wahrscheinlichkeitsfunktion, Verteilungsfunktion, Dichtefunktion, Binomialverteilung, Galton-Brett, Hypergeometrische Verteilung, Poisson-Verteilung, Gaußsche Normalverteilung, Standardnormalverteilung, Fehlerfunktion, Quantile, Mehrdimensionale Verteilungen, Randverteilungen, Chi-Quadrat-Verteilung, Gamma-Funktion, Student-t-Verteilung
6. Angewandte Statistik, Stichprobe, Mittelwert, Standardabweichung, Varianz, Spannweite, Median, Modalwert, Ausreißer, Vertrauensintervall
7. Interpolationsverfahren, Kennlinie, Look Up Table, Lineare Interpolation, Kubische Interpolation, Spline-Interpolation
8. Mehrdimensionale Interpolation, Nearest-Neighbor-Interpolation
9. Korrelation, Regression, Least Squares, Korrelationskoeffizient, Irrtumswahrscheinlichkeit, Nichtlineare Regression
10. Simulation, Dynamische Systeme, Dämpfung, Eigenfrequenz, Übertragungsfunktion, Zustandsraum, Sprungantwort
11. Optimierung, Identifikation, Kostenfunktion
12. Zufallszahlen, Sortieralgorithmen, Periodenlänge, Straight-Insertation, Shell's Method, Quicksort, Heapsort, Indexieren, Ranking
13. Matrizeneigenschaften, Spezielle Funktionen, Quadratische Matrix, Diagonalmatrix, Symmetrische Matrix, Hermitesche Matrix, Reelle Matrix, Singuläre Matrix, Orthogonale Matrix, Unitäre Matrix, Positiv definierte Matrix, Hadamard-Matrix, Hankel-Matrix, Hilbert-Matrix, Pascal-Matrix, Toeplitz-Matrix, Vandermonde-Matrix, Hessenberg-Matrix
14. Matrizeninversion, Gauß-Jordan-Zerlegung, Pivotisierung, LU-Zerlegung, Cholesky-Zerlegung, QR-Zerlegung
15. Singulärwert-Zerlegung, Singulärwerte, Singulärvektoren, (Pseudo-)Inversion, Nullraum, Wertebereich, lineare Abhängigkeiten
16. Schnelle Fourier-Transformation, Polynommultiplikation, Faltung, zero padding, Autokorrelation, Leistungsdichte, Nyquistfrequenz, Bartlett-Fenster, digitale Filter
17. Partielle Differenzialgleichungen, Wellengleichung, Diffusionsgleichung, Poissongleichung, Anfangsbedingungen, Randbedingungen, Animation
18. Numerische Lösung partieller Differenzialgleichungen, hyperbolische PDG, parabolische PDG, elliptische PDG
19. Differenzial-algebraische Gleichungen, Massenmatrix, Zwangsbedingungen, Algebraic Constraint, Minimalrealisierung
20. Randwertprobleme, Shooting-Methode, Relaxationsmethode

1. Space curves, Parameter representation, Tangent vectors, Curvature
2. Scalar and vector fields, Gradient, Divergence, Curl, Contour lines, Directional derivative, Source free vector fields, Irrotational vector fields, Laplace operator, Laplace equation, Poisson equation
3. Line integrals, Scalar potential, Conservative fields
4. Combinatorics, Probability, Permutation, Combination, Variation, De Morgan's rules, Random numbers, Histogram, Probability diagram
5. Distributions, Probability function, Distribution function, Density function, Binomial distribution, Galton board, Hypergeometric distribution, Poisson distribution, Gaussian normal distribution, Standard normal distribution, Error function, Quantile, Multidimensional distributions, Marginal distributions, Chi-square distribution, Gamma function, Student-t distribution
6. Applied statistics, Sample, Mean, Standard deviation, Variance, Range, Median, Mode, Outliers, Confidence interval
7. Interpolation, Characteristic curve, Look Up Table, Linear interpolation, Cubic interpolation, Spline interpolation
8. Multidimensional Interpolation, Nearest-Neighbor-Interpolation
9. Correlation, Regression, Least Squares, Correlation coefficient, Error probability, Nonlinear regression
10. Simulation, Dynamic systems, Damping, Natural frequency, Transfer function, State space, Step response
11. Optimisation, Identification, Cost function
12. Random numbers, Sorting algorithms, Period length, Straight-Insertation, Shell's Method, Quicksort, Heapsort, Indexing, Ranking
13. Matrix characteristic, Special Functions, Quadratic matrix, Diagonal matrix, Symmetric matrix, Hermitian matrix, Real matrix, Singular matrix, Orthogonal matrix, Unitary matrix, Positive definite matrix, Hadamard matrix, Hankel matrix, Hilbert matrix, Pascal matrix, Toeplitz matrix, Vandermonde matrix, Hessenberg matrix
14. Matrix inversion, Gauss-Jordan decomposition, Pivoting, LU decomposition, Cholesky decomposition, QR decomposition
15. Singular value decomposition, Singular values, Singular vectors, (Pseudo-) inversion, Null space, Range, Linear dependencies
16. Fast Fourier transform, Polynomial multiplication, Convolution, Zero padding, Autocorrelation, Power density, Nyquist frequency, Bartlett window, Digital filters
17. Partial differential equations, Wave equation, Diffusion equation, Poisson equation, Initial conditions, Boundary conditions, Animation
18. Numerical solution of partial differential equations, Hyperbolic PDE, Parabolic PDE, Elliptic PDE
19. Differential-algebraic equations, Mass matrix, Constraints, Algebraic Constraint, Minimal realization
20. Boundary value problems, Shooting method, Relaxation Method