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 |
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Approving CModule | HIM_MaCSN, HIM_MaET, HIM_MaTIN |
Responsible |
Prof. Dr. Heiko Knospe
Professor Fakultät IME |
Valid from | summer semester 2021 |
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 |
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 |
Details | Written Exam |
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Minimum standard | Passing the exam |
Exam Type | EN Klausur |
Goal type | Description |
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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 |
Skills | - |
Type | Attendance (h/Wk.) |
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Lecture | 3 |
Exercises (whole course) | 1 |
Exercises (shared course) | 0 |
Tutorial (voluntary) | 0 |
none |
Accompanying material | Lecture Notes, Exercises and Solutions |
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Separate exam | No |
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