Learning objectives
Formative purposes:
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. In addition he will have acquired the basic notions of differential equations, curves, differential calculus for functions of two variables and surfaces.
Applying knowledge:
At the end of the course the student should be able to apply his knowledge to solve differential equations and analyse some stability models for buildings, to draw and study curves in plane, to draw curves in space, to represent a functions of two real variables as a surface in space, to calculate the tangent plane.
The student 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 deal with a new problem and the skill to plan the solution.
At the same time he should have developed the precision in organizing 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
Prerequisites:
The notions of Mathematical Analysis I, Geometry and Algebra of the first year courses, are very useful.
Course unit content
Topics:
1. ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
2. CURVES IN PLANE AND SPACE
3. FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES IN SPACE
Full programme
DERIVATIVES, INTEGRALS, AREAS IN PLANE
GRAPHS OF ELEMENTARY FUNCTIONS, TRIGONOMETRY
CENTRE OF GRAVITY OF GEOMETRICAL PLANE FIGURES
VECTOR CALCULUS
ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
CURVES IN PLANE AND SPACE
CURVATURE
FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES IN SPACE
Bibliography
Reference books:
A.Coscia, Analisi Matematica, Libreria Santa Croce (Parma, 2017)
Teaching stuff (on the platform ELLY):
Exercises and previous years' examinations with solution (from 2013-14 to 2017-18).
Teaching methods
Teaching methods:
The course is organised into a series of frontal lessons at the blackboard (four hours a week, up to the scheduled 30 hours), practices (two hours a week) and six hours of laboratory activities in the lecture hall. The course is based on the concepts (given in an intuitive and applicative way) and on the applications and calculus. Each student individually is advised to do at home some exercises and the teacher will follow the progress using a series of revisions.
Assessment methods and criteria
Method of testing learning:
The course (3CFU) constitutes one of the two parts of the Laboratory of Structures (12CFU), the other part is Structural Mechanics (9CFU). The student must pass both tests (each test is passed with a final mark of minimum 18/30). The final mark of the entire Laboratory is computed by the weighted mean (on CFU) of the marks of the two parts.
The final test of the Course of Laboratory of Structures (part of Mathematics of Structural Mechanics) consists of a written and oral test at the end of the course which is weighted as follows:
(10%) Theoretical questions (knowledge)
(90%) Practical exercises (applying knowledge)
The theoretical questions concern comprehension of the concepts.
Instead of the final test, the student will be allowed to substain two written tests in itinere.
Other information
Other information:
This course (3CFU) constitutes one of the two parts of the Laboratory of Structures (12CFU) and it is mandatory for all students in Architecture.
Attending to the course is mandatory and checked.
