Course
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 |
| Responsible |
Prof. Dr. Heiko Knospe
Professor Fakultät IME |
| Level | Master |
| Semester in the year | summer semester |
| Duration | Semester |
| Hours in self-study | 78 |
| ECTS | 5 |
| Professors |
Prof. Dr. Heiko Knospe
Professor Fakultät IMEProf. Dr. Hubert Randerath Professor Fakultät IMEProf. 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 |
Literature
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
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
Details
Written ExamMinimum standard
Passing the examExam Type
Written ExamLearning goals
Knowledge
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
Optimization
- 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
- 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
Optimization
- 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
Skills
-
Expenditure classroom teaching
| Type | Attendance (h/Wk.) |
|---|---|
| Lecture | 3 |
| Exercises (whole course) | 1 |
| Exercises (shared course) | 0 |
| Tutorial (voluntary) | 0 |
Special literature
keine/none
Special requirements
none
Accompanying material
Lecture Notes, Exercises and Solutions
Separate exam
none
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