Politecnico di Torino
Mathematical Analysis II
02KXULI
Iowa State Course Substitution
Calculus III
MATH 265
Course Info
International Credits:
6.0
Converted Credits:
3.5
Semester:
spring
Country:
Italy
Language:
English
Course Description:
Politecnico di Torino
Academic Year 2017/18
02KXULI
Mathematical analysis II
1st degree and Bachelorlevel of the Bologna process in Automotive Engineering  Torino
Teacher Status SSD Les Ex Lab Years teaching
Como Giacomo A2 INGINF/04 50 0 0 1
SSD CFU Activities Area context
MAT/05 6 A  Di base Matematica, informatica e statistica
Subject fundamentals
This course first completes the theory of functions of one variable which was developed in Mathematical Analysis, presenting the basic
concepts of numerical series, power series and Fourier series. The basic notions of the Laplace transform are also presented here. The
course then presents basic topics in the mathematical analysis of functions of several variables. In particular, differential calculus in
several variables, the theory of multiple integration, line, and surface integration.
Expected learning outcomes
Understanding of the subjects of the course and computational skill. Familiarity with the mathematical content of engineering
disciplines.
Prerequisites / Assumed knowledge
The topics contained in the courses of Mathematical Analysis I and Linear Algebra and Geometry. In particular, limits, sequences,
differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.
Contents
Laplace transform.
Definition and convergence criteria for numerical series. Power series. Taylor series. Fourier series.
Review on vectors and elements of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and
directional derivatives, Jacobian matrix. Differentiability, gradient and tangent plane. Second derivatives, Hessian matrix. Taylor
polynomial. Critical points, free extrema.
Double and triple integrals, center of mass. Length of a curve and area of a graph. Line and surface integrals (graphs only), circulation
and flux of a vector field.
Conservative vector fields. Green, Gauss and Stokes theorems.
Delivery modes
Theoretical lessons: 50 hours. Exercise hours: 30 hours. Theoretical lessons are devoted to the presentation of the topics, with
definitions, properties and the proofs which are believed to facilitate the learning process. Every theoretical aspect is associated with
introductory examples. The exercise hours are devoted to the analysis and the methods required for solving exercises with the aim of
preparing the student to the exam.
Texts, readings, handouts and other learning resources
The following textbook covers the topics of the course:
 C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer, 2014.
Other material will be availaible on the Portale della Didattica.
Assessment and grading criteria
The goal of the exam is to test the knowledge of the candidate on the topics included in the official program of the course and to verify
the computational and theoretical skills in solving problems. Marks range from 0 to 30 and the exam is succesful if the mark is at least
18.
The exam is written and consists of 7 exercises with closed answer and one exercise with open answer on the topics presented in the
course. Questions cover also theoretical aspects.
Servizi per la
didattica
PORTALE DELLA DIDATTICA
10/22/2017 Gestione Didattica  Politecnico di Torino
https://didattica.polito.it/pls/portal30/sviluppo.guide.visualizza?p_cod_ins=02KXULI&p_a_acc=2018&p_lang=EN 2/2
The exam lasts two hours. During the exam it is forbidden to use notes, books, exercise sheets and pocket calculators.
There will be an oral exam only if required either by the teacher or by the student (in the last case only if the written exam’s grade is
greater than or equal to 18/30).
Review
 Evaluation Date:
 December 20, 2017
 Evaluated:
 James Wilson
 Comments:

Also covers series topics from our 166, introduces Laplace Transforms.