
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
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
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 openended and/or multipleanswer 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 Part A is withdrawn 30 minutes after the start of the examination.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, oneoff 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:
EXERCISE:
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).
TEXTBOOKS:
Mathematical Analysis, Michiel Bertsch, Roberta Dal Passo and Lorenzo Giacomelli, McGrawHill (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.

Bramanti, Marco, Esercitazioni di analisi matematica 2. Bologna: Esculapio, 2012. (Consigliato)


