To show the organization of the course that includes this module, follow this link Course organization
Aim of this course is to present, both from a theoretical and an empirical point of view, the main methods of calculus and linear algebra. The educational objectives have been developed with reference to Dublin descriptors, they are consistent with those characterizing the 1st cycle degree program in which the course is inserted and have been defined in coordination with those of Statistics module, with which it forms a unique course.
More specifically, students who successfully complete this course will be able to:
- determine the main characteristics of a function and sketch its graph;
- differentiate a function and solve simple geometrical problems;
- integrate a function and solve simple geometrical problems;
- solve simple differential equations;
- calculate matrix determinants and inverse matrix;
- solve a linear system.
By means of a gradual learning process, linking the contents of this course with the educational objectives characterizing the 1st cycle degree programs in which the course is inserted, students will acquire the methodological and applied knowledge about the basic concepts of Mathematics necessary to prosecute their studies.
(PREREQUISITES: Algebraic, exponential and logarithmic equalities and inequalities.)
1) Functions. Limits. Continuity.
2) Derivation and differentiation of functions. Rolle's, Lagrange's and de l'Hospital's theorems and their consequences. Applications and examples.
3) Functions and their graphs. Function's graph and linear transformations. Applications to natural sciences.
4) Integration of functions of a single real variable. Applications and examples.
5) Simple examples of differential equations.
6) Linear systems and matrices: determinants, inverse matrix, Applications to natural sciences.
Each topic is discussed both from a theoretical and an empirical point of view, with special focus on applications.
(notes and slides available at link https://app.box.com/s/t2jamq852r8j93qhhxomjy4rmckmh5vy )
Students are evaluated by means of a written comprehensive examination, composed of exercises and questions. A time of 2 hours is scheduled. The grades are on a scale of 30.
Students who attend lessons can decide to divide the exam in two parts, to be done before the class ends. A time of 2 hours is scheduled for each part and the grades are on a scale of 30. In that case, the mark of Mathematics will be calculated as the average of the scores obtained in the two different parts; in the case of a non-integer result, the mark is rounded upward.
Rules for defining the final grade of the Mathematics and Statistics course, which summarizes the tests carried out in the two modules:
(1) A module is successfully completed if the student achieves a score of at least 15/30.
(2) The examination of Mathematics and Statistics shall be passed only if both modules are successfully completed, provided that the average of the two scores, calculated as shown in (3), is not less than 18/30.
(3) The final mark is calculated as the average of the scores obtained in the two modules weighted by the number of credits; in the computation of the average, at 30 cum laude obtained in a module is assigned a score of 31; in the case of a non-integer result, the mark is rounded upward; in the case of an average of at least 30, the final mark will be 30 cum laude.