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