This course provides a basic, albeit rigorous, knowledge of mathematical tools on: sequences, series, real functions, differential and integral calculus, ODEs. In general, there will be much emphasis on concepts and main results, together with several examples and exercises. Only a few proofs will be treated in full details. At the end of the course, the students should be able to: - provide computations on limits, derivatives, integrals, differential equations, series - provide simple logical-deductive reasonings.
Course Prerequisites
Numerical sets, equations and inequalities, trigonometry, elementary functions.
Teaching Methods
The course is made of lectures and exercise sessions. Lectures provides concepts and results, by means of definitions, theorems, examples. Some proofs are given, to develop logical-deductive skills. Exercise sessions provide solutions of exercises requiring both calculus and reasoning skills.
Assessment Methods
The final exam consists in a written test and an optional oral examination. WRITTEN TEST. Requires the solution of exercises and the answer to questions. During the written test the use of books, notes and electronic devices is not permitted, unless explicitly authorized. ORAL TEST. This test is mainly focused on the theoretical part of the course: definitions, fundamental examples and counterexamples, statement and proof of the theorems. It must be taken in the same session of the written exam. In case of oral examination, the final grade will be given taking into account the score obtained in the written test and the oral test.
SETS. Real numbers. Complex numbers: algebraic and trigonometrical form, exponential form, operations, roots of unity. FUNCTIONS. Invertible, even, odd, periodic,monotone functions. Elementary functions and their graphs. Limits: definitions, computations, asymptotic relations. Continuous functions and their properties. SEQUENCES AND SERIES. Limits and convergence criteria for series. DIFFERENTIAL CALCULUS. Derivative of a function: definition and applications. Basic rules for computing derivatives. Fundamental Theorems. Anti-derivative. Graph of a function: maxima and minima. De l'Hopital rule. Taylor expansion. INTEGRALS. Definition, main properties and applications. Fundamental Theorems. Computation of integrals. Improper integrals. ODEs.First order linear differential equations. Second order linear differential equations with constant coefficients.
Course Language
Italian
More information
Students can download notes and exercises, consulting office hours will be available also online.
