The course introduces to the basic concepts and techniques of differential and integral calculus emphasizing methodology and applications over the more formal aspects. The aim is to provide the students with basic tools for addressing scientific issues which can be formalized in the language and methods of calculus. At the end of the course the student must be able to demonstrate an adequate synthesis and abstraction ability, be able to recognize and produce rigorous demonstrations and be able to formalize and solve problems of moderate difficulty, limited to the syllabus of the teaching. Main topics: real numbers, sequences and series, limits, continuous functions, differential and integral calculus for functions of one real variable, introduction to ODEs, topology of the real line.
Properties of real numbers. Sequences and series. Limits. Continuous functions. Differential and integral calculus for functions of one real variable. Elementary ordinary differential equations.
Topology of the real line.
|M.Bramanti,C.D.Pagani,S.Salsa||Analisi Matematica 1||Zanichelli||2009||978-88-08-06485-1|
|Giuseppe de Marco||Analisi uno. Primo corso di analisi matematica. Teoria ed esercizi||Zanichelli||1996||8808243125|
|R.A. Adams||Calcolo Differenziale 1 - Funzioni di una variabile reale||Casa Editrice Ambrosiana|
The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program: students are exonerated from the first part of the test if they pass a mid-term test at the beginning of december. The written test evaluates the ability of students at solving problems pertaining to the syllabus of the course, and also their skills in the analysis, synthesis and abstraction of questions stated either in the natural language or in the specific language of mathematics. The written test is graded on a scale from 0 to 30 points (best), with a pass mark of 18/30.
The oral exam will concentrate mainly but not exclusively on elementary ordinary differential equations and the topology of the real line. It aims at verifying the ability of students at constructing correct and rigorous proofs and their skills in analysis, synthesis and abstraction. The oral exam is graded on a scale from -5 to +5 point, which are added to the marks earned in the written test.