Course Manual 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 |
| 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 |
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 |
Final exam
| Details | Written Exam |
|---|---|
| Minimum standard | Passing the exam |
| Exam Type | EN Klausur |
Learning goals
| Goal type | Description |
|---|---|
| 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 | - |
Expenditure classroom teaching
| Type | Attendance (h/Wk.) |
|---|---|
| Lecture | 3 |
| Exercises (whole course) | 1 |
| Exercises (shared course) | 0 |
| Tutorial (voluntary) | 0 |
Special requirements
| none |
| Accompanying material | Lecture Notes, Exercises and Solutions |
|---|---|
| Separate exam | No |
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