The course provides the students with the fundamental notions of differential and integral calculus and the foundations of the symbolic logic and discrete mathematics. The students will be able to: analyze and model problems rigorously; apply effectively mathematical-logical techniques (deduction, induction, function optimization, asymptotic analysis, elementary com-binatorics); evaluate the correctness of logical arguments and identify mistakes in deductive processes.
1) Some notions of set theory.
2) The complete ordered field of the real numbers. Subsets of R. Complex numbers.
3) Euclidean distance and induced topology on the real line. Absolute value of a real number. Cartesian plane.
4) Real functions of one real variable.
5) Polynomials and polynomial functions. Power, exponential and logarithmic functions. Trigonometric functions.
7) Limit of a function of one real variable.
8) Continuity of a function of one real variable at one point. Fundamental theorems on continuos functions.
9) Derivative of a function. Derivation rules. Fundamental theorems on differentiable functions.
10) Monotonicity of a function. Local and global minima and maxima of a function.
11) Convex functions.
12) Taylor polynomials.
13) Riemann integral. Integration rules. Improper integrals.
|M.Bramanti,C.D.Pagani,S.Salsa||Analisi Matematica 1||Zanichelli||2009||978-88-08-06485-1|
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 2019. 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.
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