CALCULUS 2

This course belongs to the curricular activities of the the Bachelor in Computer Science.
The course aims at providing students with the basic instruments of Calculus 2, concerning functions of two or more real variables, and the solution of ordinary differential equations of the first and second order.

The aim of this course is to develop skills one needs to solve differential and integral questions arising in technology, science, economics and business.

Regular and active participation in the teaching activities offered by the Course, together with independent learning activities, will enable students to:
1. (knowledge and understanding)
-- acquire knowledge and understanding regarding some basic concepts of Calculus 2 concerning two-variable functions.

2. (applying knowledge and understanding)
-- describe and use simple mathematical models governed by ODEs;
-- compute the points of minimum, maximum, and saddle points of a function;
-- draw the graph of of two-variable functions;
-- compute the integral of two-variable functions;

3. (making judgements)
-- correctly understand Math statements concerning multi-variable functions.

The students are supposed to know the main concepts of the courses Calculus 1 and Linear Algebra.

Mathematical models
Ordinary differential equations of the first and second order.
Vectorial calculus and parametric curves.
Real functions of two or more variables.
Limits and continuity in n-dimensions.
Directional derivatives.
Partial derivatives and gradient.
Higher order derivatives.
Maximum, minimum and saddle points.
Two-dimensional integrals and reduction methods; rule of change of variables.
Vectorial fields, conservative fields and line integral.

It is recommended to study on the material provided in the moodle page of the course

The following books can be helpful:
F. Sartoretto, Calcolo, e-book, McGraw-Hill Italia, 2013
G. Naldi, L. Pareschi, e G. Aletti, Calcolo differenziale e algebra lineare, McGraw-Hill Italia, Milano, 2012.
M. Bertsch, R. Dal Passo, L. Giacomelli. Analisi Matematica. McGraw-Hill, Milano 2007

The examination consists of a written test evaluating the ability of students in solving differential equations, analyze parametric curves, and solving problems related to the Mathematical Analysis for functions of two real variables.
The evaluation is performed through problems with an open answer.

During the course, students are invited to perform three tests with multiple-choice answers, which allow to give up to 3 bonus points to the grade of the exam.

To obtain a grade higher than 27 it is mandatory to take an oral exam, where the student's preparation on the theory will be evaluated. The oral exam is optional for the other students. Students with grades 15, 16 or 17 can take the oral exam to try to obtain a sufficient grade.

Classroom lessons and exercises. The moodle platform is exploited, in order to deliver supplementary material.

Italian

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