The course aims at providing students with the basic knowledge of differential and integral calculus, as well as linear algebra. In general, greater emphasis is placed on understanding the main definitions and findings. Ample space is given to examples and exercises. At the end of the course, students should be able to correctly perform calculations regarding limits, derivatives, function studies, integrals.
Course Prerequisites
The mathematical notions required for the enrollment in the Faculty of Engineering. In particular, the following topics will be considered well-known: First and second degree algebraic equations and related inequalities. Analytical geometry of the plane. Trigonometry. Exponential function and logarithms.
Teaching Methods
Lessons (hours / year in the classroom): 30 Exercises (hours / year in the classroom): 25 Practical activities (hours / year in the classroom): 0
Assessment Methods
The exam lasts two hours and thirty minutes, and consists of a written test and an optional oral test. The written test includes: solving five exercises (first part) and answering five questions, which have a more theoretical flavour (second part). The oral exam must be taken in the same session as the written exam and includes: statements of theorems, definitions, examples and fundamental counterexamples.
Texts
V. Villani, G. Gentili, Matematica - Comprendere e interpretare fenomeni delle scienze della vita, Ed. Mc Graw-Hill
Contents
1. Review of set theory, numerical sets, real numbers. Averages, medians. 2. Basic arguments of linear algebra. Vectors and vector spaces, lines and planes. Matrices. Determinant. Inverse matrix. Rank. Systems of linear equations. 3. Concept of function. Field of existence, sign. Elementary functions: powers, exponentials, trigonometric functions, logarithms. Use of logarithmic scales. 4. Limits and continuity. Continuous functions and their main properties. Points of discontinuity. 5. Concept of derivative; geometric and physical interpretation. Tangent line. Increasing, decreasing, concave, convex functions. Maximums, minimums, inflections. 6. Fundamental theorems of differential calculus and their application to the study of functions. 7. Concept of integral; geometric and physical interpretation. Computation of integrals through integration methods by parts and by substitution.
Course Language
Italian
More information
Students in the categories identified by the project on innovative teaching will have the opportunity to hold receptions even at special times.
