MATHEMATICAL ANALYSIS 1
Learning outcomes of the course unit
This course aims at:
a) providing some fundamental mathematical tools, needed for the comprehension of other technical subjects;
b) developing attention, precision, logical reasoning and the ability to verify the correctness of results obtained in practical situations.
There are no real prerequisites: in the first portion of the course, some extra hours are devoted to the recovery of those elementary notions (on numbers including the four operations, equivalence of measures, minimal algebra, equations and inequations of first and second degree) which every student should really know after high school, but very often doesn't know at all.
Course contents summary
Numbers and operations; powers.
Measures (of length, surface, ...)
Equations and inequations of first and second order, rational, systems.
Polynomials and their roots.
Analytic geometry: lines, circles, fundamentals of ellipses and parabolas.
Trigonometry: radians, sine, cosine and tangent with their most common values; elementary inequalities.
Vocabulary of set and function theory, including extrema of a set.
Properties of functions: graph, injectivity, monotonicity.
Power functions and their inverses, equations and inequations.
Exponentials and logarithms: graphs and elementary properties.
Modulus: properties, equations and inequations.
Continuous functions and relevant theorems; limits; infinitesimals and use of Taylor expansions.
Derivative: definition and main theorems; graphing a function.
Integral: indefinite and definite, properties and main theorems.
Differential equations: solution of homogeneous linear equations of first and second order with constant coefficients.
E. Acerbi and G. Buttazzo, Matematica preuniversitaria di base, Pitagora
E. Acerbi and G. Buttazzo, Analisi matematica ABC vol.1, Pitagora
D. Mucci, Analisi matematica Esercizi, 1. funzioni di una variabile, Pitagora
Also available are lots of notes and solved exercises by Prof. A. Coscia, together with the text (and solution) of exams of the previous years.
Oral lessons will be integrated with practical ones and homework.
Throughout the year the student who attends the laboratory will be required to complete and if necessary correct several written assignments and to pass some intermediate tests. A written exam (in two parts, the first of which is after the first half of the course) will conclude the course.