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 dispari)
IN01123530, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
IN0506, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track FORMATIVO [001PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination ADVANCED MATHEMATICS FOR ENGINEERS
Department of reference Department of Industrial Engineering
E-Learning website
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 MONICA MOTTA MAT/05
Other lecturers ALBERTO BENVEGNU'

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/05 Mathematical Analysis 9.0

Course unit organization
Period First semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 9.0 72 153.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
18 A.A. 2018/19 matricole pari 01/10/2018 30/11/2019 MOTTA MONICA (Presidente)
MARSON ANDREA (Membro Effettivo)
ANCONA FABIO (Supplente)
17 A.A. 2018/19 matricole dispari 01/10/2018 30/11/2019 MOTTA MONICA (Presidente)
MARSON ANDREA (Membro Effettivo)
ANCONA FABIO (Supplente)

Prerequisites: The programs of the courses of Mathematical Analysis 1 and Algebra and Elements of Geometry. In particular: real numbers, functions of a real variable (limits, continuity, derivability), integral calculation in a variable, concept of vector space and linear function.
Target skills and knowledge: The course has the following knowledge and skills expected:
1. be able to autonomously parameterize curves, surfaces and solids of most common use and to correctly caculate geometric entities (tangent, normal. . . ) and integral curves of first and second species, areas of surfaces and integral surfaces, flow of vector fields, integral double and triple.
2. Be able to rigorously set up and solve optimization problems with and without constraints.
3. Know and know how to correctly apply the main Theorems of Dini on the implicit functions.
4. Know the definition of work, conservative vector field and the main properties of conservative fields. Knowing how to calculate potential.
5. Know and know how to correctly apply the Divergence Theorem and the Stokes Theorem.
6. To be able to solve linear differential equations of the second order with constant coefficients, also of parametric type.
7. To be able to define the objects of the course (e. g. curves, surfaces, etc. ) with mathematical language and to know the main theorems, understanding their meaning for the applications.
Examination methods: The examination consists of a written test, lasting 2 hours and 30, divided into two parts, with a single evaluation, Part A and Part B.
Part A: 2 or 3 open-ended and/or multiple-answer questions on the list of topics covered in the lesson. Part A is withdrawn 30 minutes after the start of the examination.
Part B: 3 or 4 exercises on the final program of the course, such as those carried out in class or assigned for home. The use of calculators is not permitted.
Assessment criteria: The evaluation criteria by which the verification of skills and knowledge acquired will be carried out are:

1. Ability to set up methodologically rigorously and correctly solve problems on the topics of the course
2. Clarity and completeness of the justifications given
3. Appropriate use of scientific language
4. Completeness of knowledge acquired
Course unit contents: 1. Parametric curves, tangent vector, length of a curve and integral curve of first species.
2. Scalar functions of multiple variables: graphs and level sets, limits, continuity and differential calculus
3. Optimization: study of maximum and minimum free problems
4. Implicitly defined functions: Dini theorems
5. Optimization: study of maximum and minimum problems with constraints, Lagrange multiplier method.
6. Parametric surfaces: normal vector and tangent plane.
7. Vector fields: work, conservative forces and potential.
8. Double and triple integrals: definition of mass and of centre of gravity.
9. Surface integrals and flows (Divergence and Stokes theorems).
10. Ordinary differential equations: second order linear equations. In the case of constant coefficients: similarity method and resonance phenomenon.
Planned learning activities and teaching methods: The teaching will be done through classroom lessons with the help of a tablet and whiteboard. Lessons will also be recorded and files (with and without audio) will be uploaded daily to the moodle platform. Homework will be assigned weekly in moodle, and solutions will be given during the lesson or in moodle.
To stimulate the constant and active participation of students will be administered weekly moodle quizzes, which can compete for the final assessment and, one-off active quizzes will be held (unevaluated) during the lessons to get feedback on the course progress.

All required topics and demonstrations will be held in class. At least one third of the lessons of the course will be dedicated to the guided development of exercises. In addition to the weekly reception, students will have a forum in moodle.
Additional notes about suggested reading: material in moodle:
-pdf and lesson recording, uploaded day by day
-Home exercises (assigned weekly), with solution
-Quiz with evaluation
-Collection of Examination Topics of Analysis Mat. 2, with solutions
-Notes on certain topics

Texts for reference:
-Exercises of Mathematical Analysis 2, S. Salsa and A. Squellati, ed. Zanichelli;
-Esercitazioni di Matematica, secondo volume parte prima e seconda, P. Marcellini e C. Sbordone, ed. Liguori (Napoli).
-Mathematical Analysis, Michiel Bertsch, Roberta Dal Passo and Lorenzo Giacomelli, McGraw-Hill (2nd edition);
-Elements of Mathematical Analysis two (simplified version for new degree courses), P. Marcellini & C. Sbordone, Liguori Publisher
-Differential Calculation 2, Functions of several variables, R. A. Adamas and C. Essex, CEA 2014
Textbooks (and optional supplementary readings)
  • Marco Bramanti, Carlo D. Pagani, Sandro Salsa, Analisi matematica 2. Bologna: Zanichelli, 2009. Cerca nel catalogo
  • Bramanti, Marco, Esercitazioni di analisi matematica 2. Bologna: Esculapio, 2012. (Consigliato) Cerca nel catalogo