Unit CALCULUS II
- Course
- Computer science and electronic engineering
- Study-unit Code
- GP003974
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- Teachers
-
- Paola Rubbioni
- Hours
- 81 ore - Paola Rubbioni
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Base
- Area
- Matematica, informatica e statistica
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Sequences and series of functions. Calculus for scalar functions of more variables. Curves and surfaces. Multiple integrals. Integrals on curves or sufaces. Differential formes. Differential equations.
- Reference texts
- M.Bramanti-C.D.Pagani-S.Salsa, Analisi Matematica 2, Zanichelli Ed., 2009
M.Bramanti, Esercitazioni di Analisi Matematica 2, Collana Progetto Leonardo - Esculapio - Bologna, 2012. - Educational objectives
- The main aim of this teaching is to provide students with the knowledge about calculus and methods of a second course of Mathematical Analysis.
Main knowlegdge acqired will be: series of functions; properties of vectorial functions in one variable; properties of scalar functions in more variables; ordinary differential equations; multiple integrals; integrals on curves; vectorial fields and surfaces.
Main competence acquired will be: study of some different types of convergences for series of functions, calculus of limits and integrals by means of series of functions; calculus of integrals on curves either for scalar functions and for vectorial fields; qualitative study of graphics and optimizations for scalar functions in two variables; calculus of the solutions for simple ordinary differential equations; calculus of multiple integrals; calculus of the area of surfaces, of the flow and of the potential for vectorial fields. - Prerequisites
- In order to understand the contents and achieve the learning objectives, the student must have successfully passed the first Mathematical Analysis exam because he must possess the following knowledge: limits, derivatives, integrals for scalar functions in a variable; numerical series.
Some topics covered in the course also require knowing how to calculate a determinant or know how to describe simple geometric objects in space. - Teaching methods
- Face-to-face lessons on all the topics of the course.
In addition to a detailed theoretical presentation, for each topic will also be carried out the related exercises that will be a model to those proposed in the examination. - Other information
- During the written test the use of: textbook is allowed; handwritten cards with their own personal notes inserted in a portalistini; sheets for draft; pens, pencils, ruler, ...
It is not possible to keep with you: bags or backpacks; smartphones or notebooks or calculators or other similar devices; books other than text.
For communications and any additional material, reference is made to the Unistudium platform. - Learning verification modality
- The verification of the profit is divided into a calculus test and a theoretical test. In the first test the student must perform some exercises in two hours to verify the knowledge and skills related to the calculation. In the second it is verified the acquisition of the method, language and fundamental theoretical knowledge of the subject; this test, lasting one hour, is divided into two parts: in the first one the student must state and demonstrate one of the theorems present in the program; in the second he must answer two questions on definitions, examples and counterexamples.
It is advisable to present yourself to the thoretical exam only if at least the 15/30 evaluation of the calculus test has been achieved. The final vote deviates from the calculus test vote for a maximum of six points.
For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa - Extended program
- Sequences and series of functions: sequences of functions, series of functions, seriess of powers and Taylor series; trigonometric series and Fourier series.
Infinitesimal calculus for functions of several variables: topology in R^n; limits and continuity; partial derivatives, differential, directional derivatives; free and bounded extremes. Generalized integrals. Multiple integrals: double integrals, change of variables; triple integrals. Curves and surfaces and integrals: parametric curves, lenght, integrals on curves, surfaces and integrals on surfaces. . Differential formes: linear differential formes, conservative vector fields, Green theorem, Stokes theorem, divergence theorem. Differential equations: equations of the first order; linear equations of the second order with constant coefficients.