ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| MATHEMATICS | MAT/05 | LEZIONI | 76 |
|
The student who successfully completes the course will be able to demonstrate a solid knowledge of the mathematical language, of analytical geometry of two and three dimensions, of calculus in one variable, of linear algebra and of the basics of probability and statistics; furthermore, the student will be aware of their importance in analyzing data and in building mathematical models.
During the written and the oral exam the student must be able to demonstrate his/her knowledge of the course material and his/her skills in solving related tasks.
Methods:
To be able to solve linear systems in any number of unknowns.
To be able to solve simple mathematical problems using calculus in one variable.
To be able to analyze and to use simple mathematical models of natural phenomena.
To be able to use simple probabilistic and statistical methods for studying natural phenomena.
During the written and the oral exam the student must be able to demonstrate his/her knowledge of the course material and his/her skills in solving related tasks.
Methods:
Students understand how to use mathematical methods for problem-solving.
Written and oral exams.
Basic concepts of Mathematics and Logics, Elementary algebra and elementary geometry.
Traditional exercise class will complete the frontal lectures. The course credit is 9.
Numbers. Equations and inequalities. Functions. Cartesian coordinate system. Vectors. Elements of analytical geometry of two and three dimensions. Linear systems and row reduction. Vector space R^n, subspaces, systems of generators, linear independence, basis, dimension. Linear transformations, matrices, product of matrices, inverse matrix, determinants. Elementary functions. Limits and continuity. Derivatives. Derivation formulas. Increasing and decreasing functions; maxima and minima. Convex and concave functions. Study of functions. Definite and indefinite integrals. The fundamental theorems of calculus. Techniques of integration. Improper integrals. Basic concepts of differential equations. The Cauchy-Kovalevskaya theorem: existence and uniqueness of solutions. Explicit solutions of simple types of differential equations.
Elements of discrete probability (probability distributions, independent events, conditional probability, binomial distribution) and of combinatorial calculus. Elements of statistics (mean, median, mode, variance, least-squares method). Elements of continuous probability (discrete and continuous random variables, mean and variance, Poisson, uniform, exponential and normal distributions).
Students are expected to attend all class sessions as listed on the course calendar. If a student misses more than 25 percent of practical classes during a course without a valid reason, he will not be allowed to the first Final exam.
There will be one midterm and final exam at the end of the semester.
