- Docente: Nicola Abatangelo
- Credits: 9
- SSD: MAT/05
- Language: Italian
- Moduli: Nicola Abatangelo (Modulo 1) Nicola Abatangelo (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Energy Engineering (cod. 0924)
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from Sep 19, 2022 to Dec 12, 2022
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from Nov 16, 2022 to Dec 21, 2022
Course contents
- BASIC LOGIC. Truth values, implications, proofs.
- REAL NUMBERS. Intervals, topology, construction of R, inf and sup.
- COMPLEX NUMBERS. Definitions, operations, algebraic and exponential forms, modulus and argument, de Moivre formula, roots, algebraic equations.
- FUNCTIONS. Definition, properties, composition, inversion, sequences, real functions of one variable.
- LIMITS. Convergent sequences, thereoms about limits of sequences (uniqueness, comparison,...) monotone sequences, limits of real functions of one variable, theorems about limits of real functions.
- CONTINUITY. Definition, theorems (Weierstrass, Bolzano, intermediate values,...), continuity of the composition, change of variables, discontinuities.
- DIFFERENTIAL CALCULUS. Derivatives and their calculus, mean value theorem, monotonicity test, critical points, higher order derivatives, convex functions, Taylor formula and its applications.
- INTEGRAL CALCULUS. Riemann integral, preperties (linearity, additivity, monotonicity, mean value,...), primitives, the fundamental theorem, theorems on calculus (by parts, change of variables), generalized integrals, convergence criteria.
- LINEAR DIFFERENTIAL EQUATIONS. Solutions to first and second order equations, Cauchy problems, extensions.
Readings/Bibliography
- G.C. Barozzi, G. Dore, E. Obrecht. Elementi di Analisi Matematica - Volume 1, Zanichelli (2009).
- M. Bramanti. Esercitazioni di Analisi Matematica 1, Esculapio (2011).
Teaching methods
Frontal lectures to explain the basic notions, examples, and counterexamples.
Exercises solved by the teacher.
Additional exercise sheets for personal study.
Office hours.
Assessment methods
The final examinations consists of a written test made up of two parts:
- a first one will propose some exercises;
- a second one will ask questions about the theory (definitions, theorem statements, examples, counterexamples, proofs).
The examination is passed if the grade of both parts is greater than 8/16 and if the sum of the two is greater than 18/32. The final grade is the sum of the grades in each part (31 and 32 corresponding to cum laude).
In case the written test is passed, the student can ask to also take an elective oral test. This one has to be taken in the same exam period (winter, summer, fall) as the written part.
Teaching tools
Tutoring and office hours.
Additional material will be made available on the Virtale page of the class.
Office hours
See the website of Nicola Abatangelo