MATHEMATICS AND EXERCISES-2

The teaching ISTITUZIONI DI MATEMATICA 2 is one of the basic activities of the three-year degree course in Chimica e Tecnologie Sostenibili, and allow the student to face a mathematical problem with a consistent use of the current mathematical language.
The specific goal of this teaching is the formation of the knowledge and the skills concerning the theoretical and applicative basis of the differential and integral calculus in higher dimensions. The teaching will form the basis to deal with the mathematical models developed in the other courses of the Degree.

1. Knowledge and understanding
i) To know the basic concepts of advanced Mathematical Analysis.
ii) To know how to use differential calculus in multiple variables, to understand the concepts of limits, derivatives and integrals in multiple variables.
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 the mathematical analysis in multiple variables 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.

To have achieved the goals of ISTITUZIONI DI MATEMATICA CON ESERCITAZIONI – 1, possibly (but not necessarily) having passed the exam of this teaching.
In particular, it is appropriate for the students to know the concepts and the methods of the differential and integral calculus, and the basis of the linear algebra.

Differential calculus in two variables: Limits and continuity, partial and directional derivatives, differentiability.
Study of critical points (maxima and minima) for functions in two variables.
Double integrals. Reduction formulas for double integrals on rectangles and on simple regions, change of variable for double integrals, double integrals in polar coordinates.
Some examples on triple integrals.
Curves and integrals on curves. Vector fields.
Surfaces integrals. Surfaces in R3, parameterization of a surface, normal versor to a surface, integrals on surfaces, flow of a vector field through a surface.
Vector calculus. Green Theorem, Stokes Theorem, Gauss Theorem.
First and second order linear differential equations.

M. Bramanti, C. Pagani, S. Salsa: Analisi matematica 2, Zanichelli
M. Bertsch, R. Dal Passo, L. Giacomelli: Analisi Matematica 2Ed, McGraw-Hill

M. Strani, Esercizi svolti di Analisi Matematica 2, Esculapio
M. Bramanti, C. Pagani, S. Salsa: Esercizi di analisi matematica 2, Zanichelli
L. Moschini, R. Schianchi: Esericizi svolti di Analisi Matematica
P. Marcellini, C. Sbordone: Esercizi di matematica, Vol. 2 (Tomi 1-4), Liguori

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 differential and integral calculus in two dimensions 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

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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