Mandatory pre-course: numerical sets, relations and operations, basic algebra, functions. Course: basic differential and integral calculus in R; fundamentals of vector calculus in higher dimensional space; basic ordinary differential equations; elements of probability and statistics.
The Open University, “Introduzione all'analisi”, Biblioteca EST, Mondadori, Milano (1978)
G.Prodi, “Istituzioni di Matematica”, McGraw-Hill, Milano (1994)
The Open University“Probabilita' e Statistica”,Biblioteca EST, Mondadori, Milano (1978)
Diamond e Jefferies, “Introduzione alla statistica”, McGraw-Hill, Milano (2002)
Note estratte dalle Lezioni
Learning Objectives
Knowledge acquired: Mathematical concepts and techniques (differential and integral calculus) useful in the study of the problems of applied sciences. Knowledge of basic statistical methods for the study of experimental data.
Competence acquired Basic mathematical competence (at college sophomore level) involving real functions,infinitesimal calculus, and their applications.
Skills acquired (at the end of the course):Basic skills for manipulating mathematical formulae, finding max and min values of functions, solving systems of linear equations, treating simple differential equations, evaluating statistical averages and confidence intervals of statistical distributions
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other indivual formative activities: about 140
Contact hours for: Lectures (hours): 42
Contact hours for: Laboratory (hours): 42
Contact hours for: Laboratory-field/practice (hours): 0
Seminars (hours): 0
Stages: 0
Intermediate examinations: about 8
Further information
Office hours:
Monday afternoons and upon appointment
Type of Assessment
written and oral
Course program
Sets, Relations and Functions. Useful algebraic Identities involving numbers and polynomials. Euclidean Division. Induction Principle and Proofs-by-Induction. Order and Equivalence relations. Real functions. Trigonometric and other elementary functions. The natural exponential and its applications. Differential and integral calculus of real functions. Convergence of series and other topics in Approximation Theory. Taylor's formula. Fourier series. Applications of differential and Integral calculus to graph plotting and volume computing. Basic theory of ordinary differential equations. Newton's differential Law of Motion Vector functions of two variables. Vector calculus. Stoke's Theorem. Curves of the second order in the plane. Planes in the space.Elements of descriptive and inferential statistics (random variables, Gaussian distribution, other distributions, sample means, confidence intervals). Central Limit Theorem.