Student guide Faculty of Engineering A.Y. 2008/09

Mathematical analysis I
Aim of the course
The course begins with a review of the fundamental ideas and principal calculation methods, aimed at ensuring that students coming from different courses of study all acquire the requisite familiarity with these essential basic elements.
The classic instruments of infinitesimal and differential calculus are then presented, illustrating wherever possible their applications in other disciplines.
Mathematics review course.
1. Numerical sets- sets and logic symbols.
- Numerical sets and their algebraic and topological structure (natural numbers, integers, rational numbers, real numbers).
- Subsets of the real numbers: definition of upper bound and lower bound, supremum and infimum, maximum and minimum.

2. Complex numbers.

3. Sequences and series.
- Definition of sequence and calculation of the limits.
- Numerical series and their characteristics.
- Geometric series.
- Harmonic and generalised harmonic series.
- Series with terms of alternating sign. Absolute convergence and Leibniz criterion.
- Series of powers.

4. Functions of a real variable.
- Symmetric, increasing, decreasing, periodic, limited functions.
- Maximum and minimum of a function.
- The elementary functions.
- Definition of compound and inverse functions.
- Limits of functions.
- Continuity.
- Derivative and differential.
- Elasticity
- Rules of differential calculus.
- Searching for local or global maxima and minima.
- Higher order derivatives.
- Convex or concave functions.
- Study of a function.
- Taylor - Mac Laurin series.

5. Indefinite integral.
- Definition of primitive and the indefinite integral.
- Rules of integration: by decomposition, by parts, by substitution.
Assessment will be by written and oral examination.
There will also be two intermediate progress tests: the first to be taken during the mid-semester break, and the second at the end of the course.
Reading list
Bramanti M., Pagani C. D., Salsa S., Matematica, Zanichelli.
Salsa S., Squellati A., Esercizi di Matematica, volume 1o, Zanichelli.
Course notes provided by the lecturer.