 ## Course Information

 Duration (hours) 39 ECTs 5 Practice Simulation Instructor(s) Assist. Prof. Vassilis Gaganis, Dr. Dimitris Marinakis

## Description

This course introduces the use of statistical tools for modeling field- and production-related data. Data mining, regression, classification, clustering and geostatistical methods (variogram, kriging interpolation, simulation) are covered.

## Syllabus

 1st Lecture Basic calculus I: Single and multidimensional functions. Function examples. Implicit functions. Plots, 2D plots, contours. 2nd Lecture Basic calculus II: Derivatives, gradient, Hessian. Expansions, Taylor series. Coordinate systems. 3rd Lecture Basic linear algebra I: Scalars, vectors, matrices, vector and matrix operations. Data matrices. Scalar-matrix analogs. 4th Lecture Basic linear algebra II: Linear systems of equations. Setup and solution. Eigenvalues, eigenvectors, eigen-decomposition. Non-linear equations. 5th Lecture Root finding: Exact vs numerical methods,classic methods, Newton-Raphson, extend to systems of equations. 6th Lecture Optimization: Classic optimization, optimality conditions, equality & inequality constraints. Numerical methods for linear, quadratic and non-linear optimization. 7th Lecture Data and its properties: Descriptive statistics, probability distributions, hypothesis testing 8th Lecture Exploratory data analysis I: Unsupervised learning, factor analysis, cluster analysis. 9th Lecture Regression I: Single and multiple variable linear regression. Closed form solutions. Residual analysis. 10th Lecture Regression II: Single and multiple variable non-linear regression. Numerical solutions. Neural nets and relevant models. 11th Lecture Classification & clustering: Discriminating functions. Class probabilities. Deterministic and statistical methods. 12th Lecture Geostatistics: Spatial analysis, kriging 13th  Lecture Differential equations: Setup of ODEs and PDEs for various engineering problems

Petroleum Engineering postgraduate program of the Technical University of Crete is a one-year, full-time program, designed to provide students with a scientific background in hydrocarbon exploration and skills in the practical aspects of petroleum engineering. The program begins in October, and leads to a Master of Science (MSc) degree. The program is run by the School of Mineral Resources Engineering.