Learning objectives
Knowledge and understanding:
At the end of the course the student will have consolidated the knowledge of Mathematical Analysis he had acquired during the first year of his degree course.
He should be able to apply his knowledge to the problems of Kinematics, to solve differential equations, to draw curves in plane and space, to represent the functions of two real variables as surfaces in space, to compute a volume by means of a double integral.
Applying knowledge:
At the end of the course the student should be able to solve exercises of different types concerning all the subjects of the course and will be in a position to apply such knowledge to technical branches.
He will have also improved his skill in hand geometric drawing and developed his space vision.
Making judgments:
On getting through the exam the student should have acquired the logic ability necessary to face a new problem and the skill to plan the solution.
At the same time he should have developed the precision in organising his work and the ability to check the credibility of the results.
Learning skills:
On getting through the exam the student should have acquired a good grounding in mathematical analysis to face, in the future, an autonomous analysis of possible applications in a study or in a project.
Prerequisites
The notions of Mathematical Analysis 1, Geometry of the first year course are very useful.
Course unit content
Topics:
1. DERIVATIVES, INTEGRALS, AREAS IN PLANE
KINEMATICS
2. CURVES IN PLANE AND SPACE
3. FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES AND SOLIDS IN SPACE
LINE INTEGRALS
4. DOUBLE INTEGRALS
5. ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
Full programme
Topics:
1. DERIVATIVES, INTEGRALS, AREAS IN PLANE
KINEMATICS
2. CURVES IN PLANE AND SPACE
3. FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES AND SOLIDS IN SPACE
LINE INTEGRALS
4. DOUBLE INTEGRALS
5. ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
Bibliography
Reference book:
N.Fusco, P.Marcellini, C.Sbordone, Elementi di Analisi Matematica 2, Liguori Editore, Napoli (2001)
Notes and exercises with solution (available in CENTRO DOCUMENTAZIONE)
Previous years' examinations with solution (available in TEACHING STUFF on CAMPUSNET)
Teaching methods
Teaching methods:
The course is organised into a series of frontal lessons at the blackboard, practical exercises and laboratory activities in the lecture hall where the students will be subdivided into groups. Each student individually has to do some exercises and the teacher will follow the progress through a series of revisions.
Assessment methods and criteria
Method of testing learning:
The skills acquired will be checked through two written examinations during the course and an oral examination at the end.
The final exam will be evaluated as follows:
written examination (80%) Practical exercises (applying knowledge)
oral examination (20%) divided into
Theoretical questions (knowledge) (10%)
Practical exercises (applying knowledge) (10%)
In case the student failed the written examinations during the course, the skills acquired will be checked through a written examination and an oral examination at the end of the course.
The final exam will be evaluated as follows:
written examination (80%) Practical exercises (applying knowledge)
oral examination (20%) divided into
Theoretical questions (knowledge) (10%)
Practical exercises (applying knowledge) (10%)
Other information
Other information:
The course (5CFU) is mandatory for all students in Architecture.
Attending to the course is strongly recommended.
