The aim of the course is to make the students learn the basic concepts and tools of advanced mathematical analysis that are necessary and required in engineering studies and later on in their profession.

Lectures

Differential geometry: curves and surfaces. Line and surface integrals of vector-valued functions. Divergence and curl of a vector field. Green’s and Stokes’s Theorem. Complex functions: limits, continuity and differentiation. Elementary and regular complex funtions. Integration of complex function. Cauchy's integral formula. Random experiment, frequencies. Elementary probability models. Probability spaces. Conditional probability and independence. Random variables. Distribution function and density function. Expected value, variance and moments. Statistical sample, empirical distribution function. Estimating the expectation and the variance. Point estimations: maximum-likelihood method. Confidence intervals. Hypothesis testing: compare means: u-test, one sample t-test, two samples t-test. Estimating the covariance and correlation. Linear regression.

Seminars

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Labs

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