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September 23, 2023


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Advanced Mathematics for Engineers 2 (Hochschule Ravensburg-Weingarten Univ.). Instructor: Professor Wolfgang Ertel. After a repetition of basic linear algebra, computer algebra and calculus, this course will deal with numerical calculus, statistics, and function approximation, which are the most important basic mathematics topics for engineers in the fields of computer science, mechatronics, and electrical engineering.

Topics covered in this course, Advanced Mathematics for Engineers 2, include: random numbers including Kolmogorov complexity and pseudo random number generators; statistics and probability including principal component analysis, estimators, the Gaussian distribution, and linear regression; function approximation: clustering, k-Means and the EM-Algorithm, and singular value decomposition; numerical integration and solution of ordinary differential equations.

Course Curriculum

  • Lecture 02 – Random Numbers: Kolmogorov Complexity, Pseudo Random Number Generators Unlimited
  • Lecture 03 – The Symmetry Test, BBS Generator (Blum Blum Shub) Unlimited
  • Lecture 04 – True Random Numbers, The Neumann Filter Unlimited
  • Lecture 05 – Linear Feedback Shift Registers, Derivation of a suitable Speedup Formula Unlimited
  • Lecture 06 – Statistics and Probability: Principal Component Analysis (PCA) Unlimited
  • Lecture 07 – Principal Component Analysis (PCA), Estimators, The Gaussian Distribution Unlimited
  • Lecture 08 – Maximum Likelihood, Linear Regression Unlimited
  • Lecture 09 – Applications of PCA (An Image Compression Example) Unlimited
  • Lecture 10 – Maximum Likelihood, Bayesian Linear Regression, Radial Basis Functions Unlimited
  • Lecture 11 – Demonstration of Galton Machine: Octave Examples Unlimited
  • Lecture 12 – Function Approximation: Clustering, k-Means and the EM-Algorithm Unlimited
  • Lecture 13 – Singular Value Decomposition Unlimited
  • Lecture 14 – Numerical Integration and Solution of Ordinary Differential Equations Unlimited
  • Lecture 15 – Numerical Integration, Numerical Differentiation Unlimited
  • Lecture 16 – Numerical Solution of Ordinary Differential Equations Unlimited
  • Lecture 17 – Numerical Solution of Ordinary Differential Equations Unlimited
  • Lecture 18 – Linear Differential Equations with Constant Coefficients Unlimited

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