MATHEMATICS AND EXERCISES - 1

The course of ISTITUZIONI DI MATEMATICA 1 is one of the basic courses of the degree program in Chimica e Tecnologie Sostenibili, and allows
the students to acquire the knowledge and understanding of the main concepts of mathematical analysis and linear algerba, 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 and basic algebra, 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 and Linear Algebra.
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 evalute the possibility of different approaches when solving mathamtical 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 trogonometry equations, knowledge of the basic mathamtical functions and their properties (powers, exponential and logarithms).
It is strongly suggested to follow PRECORSO-MATEMATICA GENERALE [CT0110].

The contents of the course can be divided into two parts:

FIRST PART
Classic elements of the mathematical analysis in one space dimension. In summary:

The powers, exponential and logarithms, trigonometry.
Functions of one real variable: definitions and their elementary properties.
Limits of functions: fundamental theorems and operations. Taylor formulas and theis applications to the limits of functions. Important limits.
Continuity of elementary functions. Vertical, horizontal and oblique asymptotes.
Differential calculus: derivatives of elementary and compositefunctions. Classical theorems of the differential calculus. Derivatives of higher order.
Study of a function and its graphical representation.
Integral calculus: indefinite and defined integrals.

SECOND PART

Linear algebra: Cartesian coordinates, vectors and products between vectors, matrices and matrix operations, systems of linear equation, vector spaces and subspaces, linear applications. Eigenvalues ​​and eigenvectors.

M. Bramanti, C. Pagani, S. Salsa: Analisi matematica 1, Zanichelli
M. Bramanti, C. Pagani, S. Salsa: Analisi matematica 1. Con elementi di algebra lineare, Zanichelli
S. Salsa: Esercizi di analisi matematica 1, Zanichelli
Notes on linear algebra (on the platform “moodle”)

The exam consists of a written test with exercises concerning all the topics studied during the classes. The exercises of the test conern also theoretical questions regarding the enunciation of mathematical definitions and theorems. In the test, the correctness of the exposure, the clarity and completeness of the justifications, the knowledge of the scientific language and the ability to use the tools of mathematical analysis and basic linear algebra will be evaluated.
The test will last between two and three hours.

Lectures: theory and exercises.
Educational material will be found in the "moodle" platform.

Italian

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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