The aim of the course is to provide students with the fundamental notions of differential and integral calculus in many variables, generalizing and mastering the notions learned in the course “Mathematical Analysis I” and employing, if needed, the notions of the other courses attended during the first year of the Bachelor in Computer Science.
At the end of the course the student must prove:
- to know and to be able to understand the tools and the advanced notions of the mathematical analysis and to use such notions for the solution of problems;
- to be able to use the notions learned in the course for the comprehension of the topics of further courses, not necessarily in the mathematical area, where the knowledge of mathematical analysis can be a prerequisite;
- to be able to choose which mathematical tool or theoretical result can be useful for the solution of a problem;
- to be able to appropriately use the language and the formalism of the mathematical analysis;
- to be able to broaden the knowledge in Mathematics, Computer Science or in any scientific area using, when needed, the notions of the course.
1) Ordinary differential equations (ODE). General integral of an ODE. Cauchy problems. Separable variable differential equations. First and second-order linear differential equations.
2) Differential calculus for functions of many variables. Graphs and level sets. Limits and continuity for functions of many variables. Topology in R^n. Partial derivatives. Unconstrained and constrained optimization.
3) Integral calculus in many variables: line integrals of a scalar field, double and triple integrals. Vector fields. Line integrals of a vector field.
4) Area of a surface and surface integrals.
|M.Bramanti,C.D.Pagani,S.Salsa||Analisi Matematica 2||Zanichelli||2009||978-88-08-12281-0|
The final exam is written and must be completed in 3 hours. Oral exams will not take place. The exam paper consists of questions and open-ended exercises. The total of the marks of the exam paper is 32. Any topic dealt with during the lectures can be examined. Students are not allowed to use books, notes or electronic devices during the exam. The mark of any exercise will take into consideration not only the correctness of the results, but also the method adopted for the solution and the precise references to theoretical results (e.g. theorems) taught during the lectures. The pass mark for the exam is 18.
A midterm exam will take place during the midterm week, according to the Computer Science Department's calendar. Students who take part to the midterm (whose total of the marks is 16) can decide to solve only the second part of the exam in any exam session till 30 September 2020. The total of the marks of the second part is 16. The final mark is given by the sum of the marks of the midterm and the second part.