MATHEMATICAL ANALYSIS
Knowledge and understanding of the language, concepts and fundamental theorems of mathematical analysis for real funztion of one real variable.
Ability to master the major computational tools (calculus), and to apply the tools of mathematical analysis to the study and resolution of problems, including the study of the relationship between the function and the graphic representation; in particular, ability to use the tool of approximation.
Real line; max and min, sup and inf in R; raw properties of functions of a real variable (monotonicity, boundedness, convexity). Elementary functions, graphical representation and properties. Limits and continuity. Derivatives (definitions, theorems, calculus, global properties). Study of the graph of a function. Approximation (Taylor''''s theorem). Integrals: definition, theorems, methods of integration. Improper integrals. Introduction to differential equations and some cases of solution and qualitative analysis.
Lecture notes on different topics of the course; available online at the web portal of the DADU
P. Marcellini, C. Sbordone, Elementi di matematica, Liguori 2004