# MATHEMATICS OF STRUCTURAL MECHANICS Course unit partition: Cognomi M-Z

2° year of course - First semester
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Course unit partition: MATHEMATICS OF STRUCTURAL MECHANICS

## 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 solve differential equations, to draw curves in plane and space, to represent the functions of two real variables as surfaces in space.
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 and Algebra of the first year course, are very useful.

## Course unit content

Topics:

1. DERIVATIVES, INTEGRALS, AREAS IN PLANE
GRAPHS OF ELEMENTARY FUNCTIONS, TRIGONOMETRY
CENTRE OF GRAVITY OF GEOMETRICAL PLANE FIGURES
VECTOR CALCULUS
2. ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
3. CURVES IN PLANE AND SPACE
4. FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES IN SPACE

## Full programme

Topics:

1. DERIVATIVES, INTEGRALS, AREAS IN PLANE
GRAPHS OF ELEMENTARY FUNCTIONS, TRIGONOMETRY
CENTRE OF GRAVITY OF GEOMETRICAL PLANE FIGURES
VECTOR CALCULUS
2. ORDINARY DIFFERENTIAL EQUATIONS
MODELS OF PILLARS AND OSCILLATIONS OF BUILDINGS
3. CURVES IN PLANE AND SPACE
4. FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES IN SPACE

## Bibliography

Reference book:
E.Acerbi, G.Buttazzo, Secondo corso di Analisi Matematica, Pitagora Editrice (Bologna, 2016)

Notes and exercises with solution (available in CENTRO DOCUMENTAZIONE)
Previous years' examinations with solution (available in TEACHING STUFF on ELLYDICATEA)

## 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. 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 course (3CFU) constitutes one of the two parts of the Laboratory of Structures (12CFU), the other part is Structural Mechanics. The student must pass both tests.

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)

Instead of the final test, the student will be allowed to substain two 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.