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intermediate written examinations and/or final written exam, oral exam optional
The course will develop a good understanding of the basic concepts of the theory of regular functions of a real variable real values. Will be introduced to the concepts of limit, continuity, differentiability, differentiability indispensable for the application of the classic theorems that allow to study the properties of the functions (maximum, minimum, flexible, asymptotes, concavity) which affect already at the level of quality graph. The course will be oriented then explore those statistics bases and probability theory that will presumably be of most interest to a student oriented to use those for the laboratory purposes.
Basic Concepts of Set Theory. Line equations and parabolas. Inequalities of grade I and II. Functions of a real variable. Maximum and Minimum. Convexity. Functions: polynomial, rational, periodic, trigonometric, exponential, logarithmic. Algebra of limits. Theorem on continuous functions. Theorems on differentiable functions. Asymptotes. Statistical distributions. Mean and variance. Linear regression. Independence, covariance and uncorrelated. Probability: Function of probability. Conditional probability and independence. Theorem of total probability and Bayes. Dimensional variables: expected values and variance. Bernoulli distribution, binomial, Poisson, Gauss. Central Limit Theorem.
theoretical and practices exercises