
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
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
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 multivariables 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: multivariables 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: 14 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, McGrawHill (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.

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

