MATHEMATICS AND STATISTICS

The course intends to provide students the basic math concepts, and will also provide the basics of differential and integral calculus that will be used in specific disciplines. Students will be stimulated in learning math methods and results and developing their ability to use the same for problem solving. There will also be given a concrete idea, through various examples and applications, about the importance of mathematics in applications.

Traditional (teacher up front) lessons.

• Sets. Operations between Sets. Relations. N, Z, Q, R.
• Goniometry, goniometric functions and first properties.
• Trigonometry, sine theorem, carnot theorem, applications to problems with right-angled triangles.
• Matrices. Determinant of a matrix. Reduced matrices. Rank of an array. Product columns. Inverse matrix.
• Linear systems. Cramer's theorem. Rouche-Capelli Theorem.
• Analytical geometry in the plain. Points. Distances, line equations, angular coefficient, properties, parallelism, perpendicularity.
• Circumference. Intersection between a straight and a circumference.
• Functions. Domain of a function. Monotonous functions.
• Limits of functions. Theorems.
• Derivative of a function and its geometric meaning. Elementary Derivatives. Deriving rules: sum of functions, function products, composite functions.
• Maximum and minumum of a function. Theorems.
• Primitive of a function. Indefinite integral. Defined Integral.

(1) M. Gionfriddo: Istituzioni di Matematiche. Tringale Editore

(2) M.Gionfriddo, B. Mtarazzo, S. Milici: Esercitazioni di matematiche. Spazio Libri.

(3) P. Marcellini, C. Sbordone: Elementi di Matematica. Liguori Editore.

(4) C. Sbordone e F. Sbordone: Matematica per le scienze della vita. EdiSES

(5) V. Villani, Matematica per discipline biomediche. Mc Graw-Hill

In linea di massima si farà riferimento al testo 1. Approfondimenti e chiarimenti si possono trovare nei testi consigliati.