Marco Abate, Matematica e statistica: le basi per le scienze della vita. McGraw-Hill Education, Milano, 2017.
The course is intended to provide university-level knowledge in mathematics and basic competencies in mathematical analysis, linear algebra and Euclidean geometry. The course aims at developing deductive and operative skills, allowing to use mathematics as a tool to study other scientific disciplines.
Basic notions of algebra and geometry taught in high school. Trigonometry. Logarithms and exponentials. Solution of algebraic, trigonometric, logarithmic and exponential equations.
Lectures and problem sessions in class.
Type of Assessment
Written and oral examination. Tests passed throughout the academic year can substitute for the written exam. Such tests may not be possible if emergency measures are taken.
Arithmetic, recalled: numbers and units of measurement; operations; scientific notation; approximations; equalities and inequalities; propagation of error; percentages.
Functions, recalled: functions; injective, surjective, bijective functions; composition and graphs; Cartesian coordinates; equations and inequations.
Analytic geometry: bound vectors; lengths and angles; planes; lines.
Linear algebra: upper triangular linear systems; bases and dimension; row reduction; operations on matrices; determinants; eigenvalues and eigenvectors.
Algebraic functions: linear functions linear programming; quadratic functions; polynomial functions; power functions; rational functions; limits and continuitity.
Transcendental functions: exponential functions; logistic functions; logarithmic functions; trigonometric functions; sinusoidal functions; sequences and series.
Differential calculus: derivatives; derivatives of algebraic functions; derivatives of transcendental functions; maxima and minima; study of functions; de l'Hôpital's rule; Taylor-series expansion.
Integral calculus: definite integral; properties of integrals; indefinite integral; integration by parts; integration by substitution; improper integrals; mean of a function.
Differential equations: introduction; the equation y'=ay+b; separation of variables; linear systems of differential equations; the equation y''=ay'+by+c.
Discrete probability: introduction; events; probability distributions; relative frequencies; probability axioms; independent events; conditional probability; combinatorics; binomial distribution.
Analysis of experimental data, mentioned: mean, median and mode; variance.