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, to evaluate the extrema of a function, 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 understand the mathematical machinery employed in non-mathematical courses.
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 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 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 ELLY)
Teaching methods
Teaching methods:
The course is organised into a series of frontal lessons at the blackboard (2/3 of the course) and practical exercises (1/3 of the course). 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 final test of the Course consists of a written 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
This course (6CFU) is mandatory for all students in Engineering.
Attending to the course is strongly recommended.
2030 agenda goals for sustainable development
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