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 should have acquired the notions of differential and integral calculus in several variables, of ordinary differential equations theory and of curves theory. The student will be in a position to understand the mathematical machinery employed in non-mathematical courses.
Applying knowledge:
Through the exercises carried out by the teacher and practices, the student should be able to apply his theoretical knowledge to solve differential equations, to analyse curves in plane and space, to study a functions of two real variables and to represent it as a surface in space, to evaluate the extrema of a function, to compute a multiple integral.
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.
Communicating skills:
The student will be able to communicate mathematical contents clearly enough and with precision, even outside a context exclusively applicative.
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 1 and Geometry (of the first year courses) are very useful.
Course unit content
Topics:
1. CURVES IN PLANE AND SPACE
2. FUNCTIONS OF SEVERAL REAL VARIABLES
DIFFERENTIAL CALCULUS
SURFACES IN SPACE
3. FREE AND CONSTRAINED EXTREMA
4. DOUBLE AND TRIPLE INTEGRALS
5. ORDINARY DIFFERENTIAL EQUATIONS
Full programme
Topics:
1. CURVES IN PLANE AND SPACE
2. FUNCTIONS OF SEVERAL REAL VARIABLES
DIFFERENTIAL CALCULUS
SURFACES IN SPACE
3. FREE AND CONSTRAINED EXTREMA
4. DOUBLE AND TRIPLE INTEGRALS
5. ORDINARY DIFFERENTIAL EQUATIONS
Bibliography
Reference books:
A.Coscia, Appunti ed esercizi di Analisi Matematica 2, Libreria Santa Croce (Parma, 2018)
E.Acerbi, G.Buttazzo, Secondo corso di Analisi Matematica, Pitagora Editrice (Bologna, 2016)
Exercises with solution (available in TEACHING STUFF on ELLY)
Previous years' examinations with solution (available in TEACHING STUFF on ELLY)
Teaching methods
Teaching methods:
The course is organised into a series of frontal lessons at the blackboard (2/3 of the course) and practices (1/3 of the course). The course is based on the concepts (given in a precise and rigorous way) and on the applications and calculus. Each student individually has to do some exercises and the teacher will follow the progress using a series of revisions.
Assessment methods and criteria
Method of testing learning:
The final test of the Course consists of a written and oral test which is weighted as follows:
(10%) Theoretical questions (knowledge)
(90%) Practical exercises (applying knowledge)
The theoretical questions concern definitions and theorems.
The exam is passed with a final mark of minimum 18/30.
Instead of the final test, the student will be allowed to substain two written tests in itinere.
Other information
Other information:
This course (6CFU) is mandatory for all students in Engineering.
Attending to the course is strongly recommended.
