D3a - Dipartimento di Scienze Agrarie, Alimentari e Ambientali - Guida degli insegnamenti (Syllabus)
Mathematics Program :
Real Function Theory of a real variable. Elementary functions. Limited functions, extrema of a real function. Monotonic and invertible functions.
Definition of limit and calculation of elementary limits. Asymptotes of a real function. Continuous functions and their fundamental properties. Continuity on intervals. Introduction to the concept of derivative: growth rates. Geometric meaning of the first derivative. Calculation of first derivatives and successive derivatives for elementary functions. Operations with derivatives. Derivatives of composite functions. Fermat’s Theorem for stationary points. De L’Hopital Theorem. Second derivatives and analysis of convexity and concavity of a real function. Inflection points. Study of an analytical function with its approximate graphic
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Introduction of the integration theory. Concept of primitive or antiderivative, or indefinite integral of a continuous function and its fundamental properties. Geometric meaning of integral as area under the curve of a continuous and nonnegative function defined on closed interval. Properties of definite integrals. First Fundamental Theorem of Calculus. Integrals of elementary functions and integration techniques.
Introduction of Probability Theory. Random experiments. Sample space and events. Probability definitions and principal properties, conditional probability. Law of Total Probability and Law of composed Probability. Introduction to the concept of random variable: one dimensional, discrete and continuous random variables. Normal Distribution of Gauss.
Written and oral exams
E. BALLATORI, L. FERRANTE, Introduzione alla Biomatematica, Ed. Margiacchi-Galeno.