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

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
Syllabus
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
Examinations
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.