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Analisi Matematica 2 (BIO)
Mathematics 2
Cristina Marcelli

Seat Ingegneria
A.A. 2015/2016
Credits 9
Hours 72
Period II
Language ENG

Prerequisites
Infinitesimal, differential and integral calculus for one-variable functions; linear algebra, analytic geometry in the plane and space

Learning outcomes
At the end of the course the student will have acquired basic theoretical skills and expertise on differential and integral calculus of multi-variable functions and will be able to problems and exercises.

Program
Linear ordinary differential equations; Laplace tranform in R and its applications in solving systems of linear ordinary differential equations. Infinitesimal and differential calculus for functions of several variables, free maxima and minima for two-variables functions. Multiple integrals: reduction formulas, change of variables. Curves in the plane and in the space, integration on a curve. Vectorial fields: work along a curve, conservative fields and their characterization by means of potentials. Green formulas and applications. Regular surfaces in the sapce. Area of a surface. Integration over a surface. Stokes formula. Sequences, funzions and series in the complex field. Analytic funzions. Integrals over a curve in the complex field. Laurent series and calssification of the singularities. Residue Theorem and calculus of improper integrals by the residue method.

Development of the examination
LEARNING EVALUATION METHODS
The learning evaluation method consists of two parts: -a written test, consisting in solving some exercises on topics of the course, within two or three hours,according to the type of the task; -an oral test, consisting in the discussion about some topics of the course. In order to take the oral examination, it is mandatory to achieve an assessment not less than 18/30 in the written test. The oral examination can be taken within three weeks from the date of the written test. In the case of negative result in the oral exam, the student has to repeat the written test too

LEARNING EVALUATION CRITERIA
To successfully overcome the assessment of learning, the student is required to demonstrate, through the trials described above, to understand the concepts presented in the course, to be able to make comparisons between them, to be able to set up and solve a problem through the logical-deductive method.

LEARNING MEASUREMENT CRITERIA
For each of the tests specified before it is assigned a score between zero and thirty. The overall grade is derived from the comparative evaluation of both tests and it is not greater than 6/30 in addition to the assessment achieveed in the

FINAL MARK ALLOCATION CRITERIA
In order to obtain a positive evaluation, the student must pass the written test and then achieve a sufficient judgment in the oral test. The highest rating is achieved by demonstrating a thorough understanding of the course. Praise is given to students who, having done all the tests so correctly, have demonstrated a particular brilliance in the oral and in the written assignments.

Recommended reading
Hass-Weir-Thomas, ”Analisi Matamatica 2”, Pearson

Courses

• Ingegneria Biomedica (Corso di Laurea Triennale (DM 270/04))