HIM - Advanced Mathematics

PDF Course Catalog Deutsche Version: HIM

Version: 3 | Last Change: 28.09.2019 11:58 | Draft: 0 | Status: vom verantwortlichen Dozent freigegeben

Long name Advanced Mathematics
Approving CModule HIM_MaCSN, HIM_MaET, HIM_MaTIN
Prof. Dr. Heiko Knospe
Professor Fakultät IME
Level Master
Semester in the year summer semester
Duration Semester
Hours in self-study 78
Prof. Dr. Heiko Knospe
Professor Fakultät IME

Prof. Dr. Hubert Randerath
Professor Fakultät IME

Prof. Dr. Beate Rhein
Professor Fakultät IME
Requirements Differential and integral calculus and linear algebra (Bachelor-level mathematics)
Language German and English
Separate final exam Yes
K. Burg, H. Haf, F. Wille, A. Meister, Vektoranalysis - Höhere Mathematik für Ingenieure, Naturwissenschaftler und Mathematiker, Springer Vieweg
E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons
L. Papula, Mathematik für Ingenieure und Naturwissenschaftler Band 3, Springer Vieweg
R. E. Walpole, R. H. Myers, S. L. Myers, K. Ye, Probability & Statistics for Engineers & Scientists, Prentice Hall
S. M. Ross, Probability and Statistics for Engineers and Scientists, Elsevier
S. M. Ross, Stochastic Processes, John Wiley & Sons
U. Krengel, Einführung in die Wahrscheinlichkeitstheorie und Statistik
A. Koop, H. Moock, Lineare Optimierung, Springer
R. Reinhardt, A. Hoffmann, T. Gerlach, Nichtlineare Optimierung, Springer
M. Ulbrich, S. Ulbrich, Nichtlineare Optimierung, Birkhäuser
Final exam
Written Exam
Minimum standard
Passing the exam
Exam Type
Written Exam

Learning goals

A combination of:
- Vector Analysis
- Probability Theory, Statistics and Multivariate Statistics
- Stochastic processes
- Optimization

Vector Analysis
- Vector Spaces
- Scalar and Vector Functions
- Differential Operators
- Line Integrals
- Double Integrals
- Triple Integrals
- Change of Variables
- Surface Integrals
- Divergence Theorem
- Theorem of Stokes
- Maxwell Equations

Probability and Statistics
- Descriptive Statistics
- Two-dimensional Data
- Simple Linear Regression
- Probability Spaces
- Random Variables
- Expectation, Variance, Moments
- Jointly Distributed Random Variables
- Independent Random Variables
- Covariance
- Binomial Random Variable
- Poisson Random Variable
- Uniform Random Variable
- Normal Random Variable
- Chi-Square Distribution
- t-Distribution
- Central Limit Theorem
- Distributions of Sampling Statistics
- Confidence Intervals
- Hypothesis Testing
- t-Test, f-Test, Chi-Square Test
- Overview of various Tests

Multivariate Statistics
- Analysis of multidimensional data
- Multivariate Random Variables
- Matrix decompositions, Singular Value Decomposition (SVD)
- Factor analysis, Principal Component Analysis (PCA)
- Multiple Linear Regression

Stochastic Processes
- Discrete and continuous time processes
- Random walk
- Markov chain
- Poisson process
- Queuing theory

- Linear Programming
- Unconstrained Optimization: Gradient method, Newton's method, Trust Region method
- Constrained Optimization: Karush–Kuhn–Tucker (KKT) conditions, Lagrange multipliers, Penalty and Barrier functions
- Special optimization problems: Mixed Integer Nonlinear Programming, Nonlinear Stochastic Optimization

Expenditure classroom teaching
Type Attendance (h/Wk.)
Lecture 3
Exercises (whole course) 1
Exercises (shared course) 0
Tutorial (voluntary) 0
Special literature
Special requirements
Accompanying material
Lecture Notes, Exercises and Solutions
Separate exam

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