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 2018
- Offered
- 2018/19
- Learning activities
- Base
- Area
- Matematica, informatica e statistica
- Sector
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Series of functions. Calculus for vectorial functions of one variable. Calculus for scalar functions of more variables. Multiple integrals. Generalized integrals. Integrals of scalar functions on curves. Vector fields and their integrals on curves. Regular surfaces and integrals on surfaces. Ordinary differential equations and Cauchy problem.
- Reference texts
- M.Bramanti-C.D.Pagani-S.Salsa, Analisi Matematica 2, Zanichelli, 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 three exercises in three 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
- Series of powers and Fourier series: series of functions and total convergence; series of powers and Taylor series; trigonometric series and Fourier series.
Infinitesimal calculus for vector functions in one variable: support; limits; continuity and derivability; curve definition; equivalent curves.
Infinitesimal calculus for scalar functions of several variables: graphs and level sets; limits and continuity; topology in R^n and properties of continuous functions; partial derivatives, tangent plane, differential; derivatives of higher order, hessian matrix; optimization; free and bounded extremes.
Double and triple integrals: double integrals, reduction formulas, change of variables (in particular, polar coordinates); triple integrals, reduction formulas (for wires), change of variables (in particular, cylindrical and spherical coordinates).
Integrals in a generalized sense: remarkable cases; sufficient conditions for integrability in a generalized sense.
Line integrals of I and II species: regular curves; length of a curve arc; line integrals of I species; line integrals of II species; work of a vector field; Gauss-Green formula in the plan.
Surface integrals of I and II species: regular surfaces; area of ¿¿a surface; surface integrals of I species; surface integrals of II species; flow of a vector field; divergence theorem and Stokes formula.
Ordinary differential equations: differential models; equations of the first order (with separable variables, of Manfredi, linear); linear equations of the second order; Cauchy problem.