The aim of the course is to provide basic knowledge preparatory to other courses that require mathematical methods and tools.
The knowledge of mathematical basic tools useful in physical problems modelling. The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting. At the end of the course the student will be able 1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. Infimum and Supremum of a set, continuity and differentiability of a function ); 2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis; 3. to select the suitable mathematical tools in problem solving; 4. to solve problems with deductive reasoning.
The knowledge of mathematical basic tools useful in physical problems modelling. The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting. At the end of the course the student will be able
1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. Infimum and Supremum of a set, derivative, integral, line integral, Existence and Uniqueness theorems for differential problems );
2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis;
3. to set up problem solving with an intuitive approach;
4. to select the suitable mathematical tools in problem solving;
5. to solve problems with deductive reasoning.
Elementary Algebra, Trigonometry and Analytic Geometry in the plane.
The course consists of 52 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Several intermediate tests are provided.
Students have several exercises at their disposal on Aulaweb.
Students with SLD, disability or other regularly certified special educational needs are advised to contact the professor and the University referent at the beginning of the course to agree on teaching methods that, in compliance with the course objectives, take into account the individual learning requirements.
Real numbers and the real line. Cartesian coordinates in the plane. Sequences: properties and elementary examples. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function. L’Hopital’s rule. Taylor’ formula and its applications.
Main books
T. Zolezzi: Dispense di analisi matematica I. C. Canuto – A. Tabacco: Analisi Matematica 1. Teoria ed esercizi. Unitext, Springer – Verlag. 2014 F. Parodi – T. Zolezzi: Appunti di analisi matematica. ECIG, 2002 R. Adams: Calcolo differenziale I. Funzioni di una variabile reale. Casa ed. Ambrosiana, 1992.
Practices
M. Baronti – F. De Mari – R. van der Putten – I. Venturi: Calculus Problems. Springer 2016 M. Pavone: Temi svolti di analisi matematica I. Marcellini-Sbordone: Esercitazioni di matematica, I volume S. Salsa – A. Squellati: Esercizi di Matematica, volume 1.
Ricevimento: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed on February 2025. The e - mail address is : robertus.van.der.putten@unige.it
Ricevimento: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed on February 2025. The e - mail address is : marco.baronti@unige.it
ROBERTUS VAN DER PUTTEN (President)
CLAUDIO ESTATICO
MARCO BARONTI (President Substitute)
Lessons start on Thursday, 26 september 2024
The exam consists of a multiple choice test and a written examination. It is necessary to be successful in the multiple choice test in order to access the written exam. To enroll the exam you must register by the deadline on the website https://servizionline.unige.it/studenti/esami/prenotazione Students with SLD, disability or other regularly certified special educational needs are advised to contact the professor and the University referent at least 15 days before each examination to agree on exhamination methods that, in compliance with the course objectives, take into account the individual learning requirements.
The aim of the examination is verifying the skills acquired by the student.
As regards the Multiple choice tests the aim is verifying the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It is necessary to be successful in the multiple choice test in order to access the written exam.
The aim of the written examination is verifying the skills acquired by the student. The problems proposed in the examination call for the choice and the application of suitable mathematical tools, besides their solution needs the skill of constructing a logical connection applying theoretical topics treated. The student must solve the exercises justifying the most important passages recalling theorems and definitions and underlying the physical and geometric interpretation of the problem.
The final evaluation depends also on the quality of the written exposition and on the ability of reasoning.
