First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
ADVANCED MATHEMATICS FOR ENGINEERS (Ult. numero di matricola pari)
INP7078338, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
IN0509, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ADVANCED MATHEMATICS FOR ENGINEERS
Department of reference Department of Management and Engineering
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge LAURA CARAVENNA MAT/05

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/05 Mathematical Analysis 6.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Examination board not defined

Prerequisites: Knowledge of the syllabus of Analisi Matematica 1 and topics in amenti di Algebra Lineare e Geometria.
More precisely: real numbers, one variable real functions (limits, continuity and differentiability), integral calculus for one variable functions, basics notions related to multi-variables functions: continuity, directional derivatives and differentiability, ), calculus with matrices, concepts of vector spaces and linear functions.
Target skills and knowledge: Aim of this course is to understand the fundamental concepts of mathematical analysis related to: multi-variables functions, both differentiability and integrability, applications to physics problems, optimization problems with and without constraints. Differential Equations.
Examination methods: The final exam consists of a written part plus a possible extra oral part.
Written exam:
this exam will be divided into two parts A e B.
It is necessary to be sufficient in both parts to pass the exams.
Part A: open questions and/or multiply choice questions mostly on the theoretic part of the program.
Part B: 1-4 exercises.
Books, cellular phones, calculators are not allowed.
Extra oral part:
If the committee will retain necessary the student could be asked to substain an extra oral part.
Assessment criteria: Both the knowledge and skills acquired by the student on the topics in the program will be evaluated.
The final grade will be calculated as an average of the grade obtained in the competence test (exercise resolution)
and in the evidence on the knowledge (knowledge and understanding of the theorems and the foundational results of the
mathematical analysis in the program, with proofs if required).
Quizzes might also be proposed during the course, which will possibly contribute to the final grade.
Course unit contents: Functions of several variables: maxima and minima of functions of several variables on open sets, Gradient, Jacobian and Hessian matrix. Maxima and minima for functions of two and three variables with or without constraints. Curves and integrals curvs of first and second types. Work, length of curves. Double and triple integrals. Surface integrals and flows; divergence theorem and Stokes. Differential equations.
Planned learning activities and teaching methods: The teaching will be done through classroom lessons using a tablet and/or blackboard. The lesson files will be loaded weekly (in moodle).
Periodically homework assignments will be assigned with a solution in class or in moodle
Moodle quizzes will be offered, weekly.
All the required topics and proofs will be held in class. At least a quarter of the course's lectures will be dedicated to guided exercises.
In addition to the weekly office hours, students will have a forum in moodle.
Additional notes about suggested reading: Auxiliary material will be updated wekly in Moodle (notes on some topics and usually transcripts of the lectures, exercises, quizzes, collections of past exams with answers, ...)
Exersice books:
-Esercizi di Analisi Matematica 2, S. Salsa e A. Squellati, ed. Zanichelli;
-Esercitazioni di Matematica, secondo volume parte prima e seconda, P.Marcellini e C.Sbordone, ed. Liguori (Napoli).
Text books:
-Analisi Matematica, Michiel Bertsch, Roberta Dal Passo e Lorenzo Giacomelli, McGraw-Hill (2a edizione);
-Elementi di Analisi Matematica due (versione semplificata per i nuovi corsi di laurea), P. Marcellini & C. Sbordone, Liguori Editore
-Calcolo Differenziale 2, Funzioni di piu' variabili, R.A. Adamas e C. Essex, CEA 2014
Textbooks (and optional supplementary readings)
  • Bramanti, Marco; Salsa, Sandro, Analisi matematica 2. Bologna: Zanichelli, 2009. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Problem based learning
  • Auto correcting quizzes or tests for periodic feedback or exams
  • Active quizzes for Concept Verification Tests and class discussions
  • Video shooting made by the teacher/the students
  • Loading of files and pages (web pages, Moodle, ...)
  • Students peer review

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Latex
  • Mathematica
  • Matlab