CALCULUS I

The course of ANALISI MATEMATICA I is one of the basic courses of the degree program in Ingegneria Fisica, and allows the students to acquire the knowledge and understanding of the main concepts of mathematical analysis, a fundamental cultural baggage in every scientific discipline. The specific goal of the course is to provide knowledge of the aforementioned subjects in order to allow students to develop the necessary skills to solve mathematical problems. A particular attention is devoted to teach how to develop a logical reasoning, which is fundamental ability to be able to approach problems of basic analysis, that are the basis of various problems in all others scientific fields.

1. Knowledge and understanding
i) To know the basic concepts of Mathematical Analysis.
ii) To know how to use infinitesimal calculus, to understand the concept of limits, derivatives and integrals.
iii) To know the definitions and the mathematics symbolism.
2. Ability to apply knowledge and understanding.
i) To know how to reason in a logical way and how to use mathematical symbolism in an appropriate way.
ii) To understand mathematics and to know how to set up a strategy to solve problems.
iii) To know how to recognize the role of mathematics in other sciences.
3. Ability to judge
i) Being able to evaluate the logical consistency of the results obtained, both in the theoretical field than in the case of concrete mathematical problems.
ii) Being able to recognize errors through a critical analysis of the method applied and through a control of the results obtained.
iii) To evaluate the possibility of different approaches when solving mathematical problems.
4. Communication skills
i) To know how to communicate what have been learned by using an appropriate terminology, also in written form.
ii) To know how to interact with the teacher and with the classmates in a respectful and constructive way, by asking coherent questions and by proposing other ways to solve a problem.
5. Learning skills
i) To know how to take notes in an effective way, selecting and collecting information according to their importance and priority.
ii) To know how to consult the books given by the teacher, and to know how to identify alternative references, also through the interaction with the teacher.
iii) Being able to exploit the concepts learned to correctly perform a mathematical problem.

Good mathematical knowledge at the level of High School and Higher Secondary School programs: algebra and elementary geometry, analytical geometry,
algebraic equations and inequalities, basic knowledge of trigonometry and of the trigonometry equations, knowledge of the basic mathematical
functions and their properties (powers, exponential and logarithms).
It is strongly suggested to follow PRECORSO-MATEMATICA GENERALE [CT0110] (see also "Assessment methods").

The contents of the course consist in classical elements of mathematical analysis of one real variable. In summary, after having recalled a few prerequisites:

Functions of one real variable: definitions and their elementary properties.
Limits of functions: fundamental theorems and operations.
Sequences and series
Continuous functions of one real variable: definitions, properties and classical theorems
Differential calculus of one real variable: properties and definitions
Integral calculus for functions of one real variable: Cauchy-Riemann integral, definite and indefinite integral, computation of integrals, generalized integrals

Reference texts:
Theory: A. Marson, P. Baiti, F. Ancona, B. Rubino: Analisi matematica 1. Teoria e applicazioni, Carocci
Exercises: S. Salsa, A. Squellati: Esercizi di analisi matematica 1, Zanichelli

Suggested texts:
Theory:
G. De Marco: Analisi Uno. Teoria ed esercizi (Terza edizione), Zanichelli.
M. Lanza de Cristoforis, Lezioni di Analisi Matematica 1, Esculapio
M. Bertsch, A. Dell'Aglio, L. Giacomelli, Epsilon 1 - primo corso di Analisi Matematica, McGraw-Hill

Exercises:
P. Marcellini, C. Sbordone: Esercizi di matematica, Vol. 1 (Tomi 1-4), Liguori
G. De Marco, C. Mariconda, Esercizi di calcolo in una variabile, Zanichelli/Decibel
M. Bramanti: Esercitazioni di Analisi Matematica 1, Esculapio

The examination consists of a written test, which includes theoretical questions (definitions, statements and some proofs which will be listed during the course), as well as exercises covering all the topics studied in class. In the written test, correctness of exposition, clarity and completeness of justifications, knowledge of scientific language and skill in using the tools of mathematical analysis will be evaluated. The written proof will last about three hours. The lecturers reserve the right to request an oral supplement.

Lectures: theory and exercises, using tools such as tablet and laptop.
Educational material will be found in the "moodle" platform.

Italian

STRUCTURE AND CONTENT OF THE COURSE COULD CHANGE AS A RESULT OF THE COVID-19 EPIDEMIC.

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding supportservices and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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