# CALCULUS 2

## Learning outcomes of the course unit

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.

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

Prerequisites:

The notions of Mathematical Analysis 1 and Geometry (of the first year courses) are very useful.

The notions of Mathematical Analysis 1 and Geometry (of the first year courses) are very useful.

## Course contents summary

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

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

## Course contents

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

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

## Recommended readings

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)

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 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.

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 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.

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 informations

Other information:

This course (6CFU) is mandatory for all students in Engineering.

Attending to the course is strongly recommended.

This course (6CFU) is mandatory for all students in Engineering.

Attending to the course is strongly recommended.