Instructors: Garyfallos Papaschinopoulos / Gesthimani Stefanidou
Course Code: TMC160
Semester: 3nd
Weekly teaching hours: 6
ECTS CREDITS: 5
Prerequisites: Mathematics I, Mathematics II
Course offered to Erasmus students: No
Course URL: https://eclass.duth.gr/courses/ TMC160/
Learning Outcomes:
The scopus of the course is to introduce the students to basic concepts concerning Probabilities, Statistics and Numerical Methods for solving algebraic equations, Linear Systems, Differential equations, e.t.c. which are necessary for all students of School of Engineering.
General Skills:
Search, analysis and synthesis of data and information,
Critical thinking
Decision making
Project design and management
Production of new research ideas
Promoting free, creative and inductive reasoning
Course Content:
Permutations and Combinations. Probability. Conditional probability. Bayes Theorem. Continuous and Discrete Random Variables. Distribution Function. Probability Density Function. Mean, Variance, Standard Deviation, Median. Distributions: Bionomical Distribution, Geometrical Distribution, Poisson Distribution, Exponential Distribution, Normal Distribution, Typical Normal Distribution. Functions of Random Variables, Central Limit Theorem. Estimation of Parameters. Method of Moments. Confidence Intervals. Testing of Hypothesis. X2 test. Regression Analysis. Confidence Intervals in Regression Analysis. Correlation Analysis.
Solutions of Equations by Iteration: Bisection Method, Fixed-Point Iteration, Newton’s Method, Secant Method. Numerical Methods in Linear Algebra: Linear Systems, Crout Method, Jacobi Iteration, Gauss-Seidel Iteration, Interpolation: Newton’s Forward Difference Formula, Lagrange Interpolation, Splines. Numerical Integration: Trapezoidal Method, Simpson’s Rule of Integration, Numerical Methods for Differential Equations: Euler Method, Runge-Kutta Methods, Method of Determined Coefficients.
Suggested Bibliography:
1. Statistics Theory and Applications, F. Kolyva-Machera, E. Bora-Santa, Ziti, 1998, ISBN 960-431-338-X
2. Probability Concepts in Engineering Planning and Design, Basic Principles (Probability Concepts in Engineering Planning & Design), A. H.-S. Ang, Wilson H. Tang, Wiley and Sons, Inc 1975, ISBN 0-471-03200-X
3. Basic Chapters of Numerical Analysis, M.N. Kesoglides, Anikoula, 2005, ISBN 960-516-024-2.
