1000726 - ISTITUZIONI DI MATEMATICHE M - Z
Expected Learning Outcomes
The objectives of the course are the following:
Knowledge and understanding: the student will learn some basic mathematical concepts and will develop both computing ability and the capacity of manipulating some common mathematical structures among which limits and derivatives for functions of real variable.
Applying knowledge and understanding: by means of examples related to applied sciences, the student will learn the central role of Mathematics within science and not only as an abstract topic. This will expand the cultural horizon.
Making judgements: the student will tackle with rigour some simple yet meaningful methods of Mathematics. This will sharpen his logical ability. Many proofs will be exposed in an intuitive and schematic way, to make them more usable also to students that are not committed to Mathematics.
Communication skills: studying Mathematics and dedicating time to guided exercitations, the student will learn to communicate with clarity and rigour both, verbally and in writing. The student will learn that using a properly structured language is the key point to clear and effective scientific, and non-scientific, communication.
Learning skills: the students, in particular the more willing, will be stimulated to examine in depth some arguments, alone or working in group.
Course Structure
The course is organized by lectures. There will be some team practices.
Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previuos statements, in line with the programme planned and outlined in the syllabus.
Learning assessment may also be carried out on line, should the conditions require it.
Required Prerequisites
Attendance of Lessons
Detailed Course Content
- Matrix. Systems of linear equations.
- Elements of vector calculus and applications tu the analytical geometry.
- General notions on numerical sets.
- Real valued functions of real variable and their limits.
- Continuous functions and their properties.
- Differential calculus for real valued functions of one real variable and its applications.
- Integral calculus for real valued functions of one real variable
Textbook Information
Notes of the Teacher.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Elements of linear Algebra (about 6 hours) | notes |
| 2 | Matrices, linear systems (about 7 hours) | notes |
| 3 | Applications of linear Algebra to Analytic Geometry (about 4 hours) | notes |
| 4 | Numerical sets (in particular, real and complex numbers (about 22 hours) | notes |
| 5 | Real functions of one real variable (generalities, elementary functions, limits) (about 10 hours) | notes |
| 6 | Continuous functions (about 5 hours) | |
| 7 | Differential calculus (about 14 hours) | notes |
| 8 | Integral calculus (about 7 hours) | notes |
Learning Assessment
Learning Assessment Procedures
In april it will be done a test (P.I.), based on the first chapters. The structure is:
T) two theorical tests
E) a technical exercise (E1) and the domain of a function (E2).
During the last classes it will be done a test (F.C.) based on the other chapters, reserved to students who have passed P.I., it has the same structure as P.I., except from E2.
Students who have already passed both P.I. and F.C. could obtain the CFU required.
The final exam consists in two sections:
T) three theoretical tests (with only one proof)
E) a technical exercise.
Students who want to reach better notes could ask for an oral exam.
Examples of frequently asked questions and / or exercises
Versione in italiano