Course Instructors: Gh. Oprisan, O. Stanasila.

Fundamental discipline indispensable to any specialized approach but it contains direct applications. Classification of partial second-order equations and some methods to solving its are presented. Basics of probability theory, mathematical statistics and the notion of stochastic process with applications are broached.

Syllabus:

• Partial second-order equations (classification and canonical form).
• Some methods of solving second-order equations.
• Probability spaces.
• Classical examples.
• Independence and conditioning  Schemes of probability.
• Random variables and distribution functions.
• Random vectors and function of random variables.
• Discrete random variables.
• Densities of probability.
• Classical probability distributions (binomial, Gaussian, Poisson, uniform etc.).
• Sequences of random variables.
• Law of large numbers, applications.
• Central limit theorem.
• Elements of mathematical statistics (selection, estimation).
• The notion of stochastic process. Markov property. Applications and examples (Poisson, birth-death, reliability etc.).