MATHEMATICAL ANALYSIS 1
LEARNING OUTCOMES OF THE COURSE UNIT
The course presents the functional notions of Mathematical Analysis highlighting the typical deductive reasoning techniques and provides basic math instruments for many teachings in the Architecture degree course.
COURSE CONTENTS SUMMARY
Set, subsets, set of parts. Principle of induction and applications. Equivalence and order relations: majorants, minorants, limitation. Functions: Injectivity, surjectivity and Images. Sequences. Monotone functions. Composition of functions and invertibility. Digression on numbers: rational numbers and real numbers and their properties. Ordered fields and absolute value. Powers with real exponent. Graphs of f(x), kf(x), f(x+h), f(x)+h, |f(x)|. Graphs of elementary functions: power, root, exponential, logarithmic function. Revision of trigonometry. Functions of a real variable. Limits, continuity (and related theorems), derivatives, differentials. Theorems of Fermat, Rolle, Cauchy, Lagrange (with demonstrations). De l’Hospital’s rule. Function graphs. Infinitesimals and infinites. Taylor-Maclaurin polynomials with Peano remainder. Definite and indefinite integrals. Integration methods. Fundamental theorem of integral calculus. Integral function. Geometric applications. Improper integrals. Convergence criteria. Definition and solving of first order linear equations.
Acerbi-Buttazzo, "Matematica preuniversitaria di base", Casa Editrice Pitagora, Bologna.
Acerbi-Buttazzo, "Analisi matematica ABC 1. Funzioni di una variabile", Casa Editrice Pitagora, Bologna.
Mucci Domenico, "Analisi matematica: esercizi", Casa Editrice Pitagora, Bologna.
Procedure for exercises: guided exercises in small groups will be carried out each week.
Examination procedure: during the course two written tests will be given valid for passing the examination, which otherwise entails a written examination and an oral one.