Student guide Faculty of Engineering A.Y. 2007/08

Mathematical Analysis II
Aim of the course
This course will deal with classical instruments of metrical, infinitesimal, differential and integral calculus.
The main aims are:
1) achieving skills of analysis, such as introducing and using rigorous discussion and analytical reasoning in order to understand symbol definition, meaning and preparing for the research of formula applicability conditions;
2) learning rigorous, appropriate and essential vocabulary;
3) preparing to meet and manage the use of quantitative methods
1. Integrals
- Definite and indefinite integrals
- Integration techniques
- Geometrical applications
- Integral function
- Generalised integrals
- Line integral
2. Vectorial space Rn
- Vectors and linear combination
- Linear dependence and independence
- Matrices and matricial calculations
- Determinant
- Inverse matrix
- Linear systems
- The Cramer method
- Matrix rank
- Rouchè-Capelli theorem
3. Real functions in n real variables
- Functions in Rn
- Partial derivatives
- Directional derivatives and gradient vector
- Two variables functions optimisation
4. Differential equation
- equation in separable variables
- Linear equation
- Constant equation and coefficients of the second order homogeneous and non homogeneous.
5. Double integral
- geometric meaning and calculation
The exam consist of a written and an oral test. During the course there will be also some written testes that will be either considered or substituted for the final exam.

Reading list
Bramanti, Pagani, Salsa, Matematica, Milano, Zanichelli, 2000.
Salsa, S., Squellati, A., Esercizi di Matematica, volume 1, Zanichelli