Unit CALCULUS II
- Course
- Computer science and electronic engineering
- Study-unit Code
- GP003974
- Curriculum
- In all curricula
- Teacher
- Anna Rita Sambucini
- Teachers
-
- Anna Rita Sambucini
- Hours
- 81 ore - Anna Rita Sambucini
- CFU
- 9
- Course Regulation
- Coorte 2022
- Offered
- 2023/24
- 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
- Differential equations. Infinitesimal calculus for vector functions; curves; line integrals. Differential calculus for functions of several variables. Multiple integrals. Vector fields. Surfaces and surface integrals. Sequences and series of functions.
- Reference texts
- .Calogero Vinti -Lezioni di Analisi Matematica II
COM Ed.
The slides of the lessons are published weekly on Unistudium - 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.
To support teaching, the Maple software and the OneNote application will be used. - 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 method of verification of the learning results of the analysis module is divided in two phases:
a written exam of 2 - 3 hours and an oral examination of more or less 40 minutes. The written test includes the solution of two/three exercises on topics covered in the program and is designed to verify the ability to correctly apply the theoretical knowledge, the understanding of the exercices proposed and the ability to communicate in writing. The oral test is designed to assess the level of knowledge and the understanding reached by the student on the contents listed in the program, this test also used for verifying the presentation skills of the student. It must be performed in the same session of the written exam.
The tests together allow to ensure the ability to:
- Knowledge and understanding,
- Apply the skills acquired,
- Exposition,
- Develop solutions.
Students with disabilities must inform the teacher of their status with a note when booking the exam (at least one week before) in order to allow for an appropriate organization of the written test - Extended program
- Differential equations: I order differential equations, II order linear differential equations with constant coefficients. Calculus for vector functions; curves; line integrals of I kind. Infinitesimal calculus for functions of several variables: topology of R^n, limits and continuity, calculus of limits, partial derivatives, differential, directional derivatives, relative maxima and minima, absolute maxima and minima. Multiple integrals: double integrals and transformation of variables, triple integrals. Vector fields: line integrals of II kind, conservative fields, Green's, Stokes's, divergence theorems. Surfaces and surface integrals. Sequences and series of functions: sequences of functions, series of functions, power and Taylor series, trigonometric and Fourier series.
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- istruzione di qualità