MATHEMATICS AND EXERCISES-2

The teaching "INSTITUTIONS OF MATHEMATICS 2" falls within the basic activities of the three-year degree course in Chemistry and Sustainable Technologies, and allows the student to tackle a mathematical problem in
his various forms, with consistent use of the current mathematical language. The specific objective of the teaching is the training of knowledge and skills regarding the theoretical and basic application foundations of differential and integral calculus, with extension to the case of functions of several variables. The taught notions will form the basis for dealing with the mathematical models developed in the other courses included in the degree course curriculum.

1. Knowledge and understanding
i) Know the basic concepts of Advanced Mathematical Analysis.
ii) How to use the differential calculus in several variables, understand the notions of limits, derivatives and integrals in several variables.
2. Ability to apply knowledge and understanding.
i) Knowing how to think logically and knowing how to use mathematical symbolism appropriately.
ii) Understanding mathematical analysis in several variables and knowing how to set up a strategy for solving problems.
iii) Knowing how to recognize the role of mathematics in the other sciences.
3. Judgment skills
i) Knowing how to evaluate the logical consistency of the results, both in theory and in the case of concrete mathematical problems.
ii) Knowing how to recognize any errors by analyzing the method applied and by checking the results obtained.
iii) Knowing how to evaluate the possibility of alternative approaches to mathematical problems.
4. Communication skills
i) Knowing how to communicate the knowledge learned using appropriate terminology, even in written form.
ii) Knowing how to interact with the teacher and peers in a respectful and constructive way, formulating coherent questions and proposing alternative ideas to solve the problems dealt with.
5. Learning skills
i) Knowing how to take notes effectively, knowing how to select and collect information according to their importance and priority.
ii) Knowing how to consult the texts indicated by the teacher, and be able to identify alternative sources of reference, also through interaction with the teacher.
iii) Knowing how to exploit the notions learned to correctly solve a mathematical problem.

Having achieved the educational objectives of INSTITUTIONS OF MATHEMATICS WITH EXERCISES - 1, possibly (but not necessarily) having passed this exam. In particular, students should be able to master the concepts and methods related to differential and integral calculus and the basic notions of linear algebra.

Differential calculus in two variables: Limits and continuity, partial and directional derivatives, differentiability. Study of critical points (maximum and minimum) for functions in two variables. Double integrals. Reduction formulas for double integrals on rectangles and on simple regions, variable change formula in double integrals, double integrals in polar coordinates. Hints to triple integrals. Curves and curvilinear integrals. Vector fields. Surface integrals. Surfaces in R3, parameterization of a surface, versor normal on a surface, surface integrals, flow of a vector field across a surface. Vector computation. Green's theorem, Rotor's or Stokes's theorem, divergence or Gauss's 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. Bertsch, A. Dall'Aglio, L. Giacomelli: Epsilon 2, 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 on all the studied topics. The exercises of the written test also include theoretical questions consisting in the enunciation of mathematical definitions and theorems. The written test will assess the correctness of the presentation, the clarity and completeness of the justifications, the knowledge of scientific language and the ability to use the tools of differential and integral calculus in two variables.
The written test will last between two and three hours.

written

18-21: Basic understanding of the essential topics. The student is able to complete standard and purely mechanical exercises (e.g., direct calculations and guided procedures). Shows significant theoretical gaps and struggles with the geometric interpretation of results or when setting up problems that fall slightly outside the usual patterns.
22-23: Adequate mastery of the main computational methods. Correctly sets up and solves most exercises, albeit with some computational inaccuracies. Theoretical knowledge is mostly memorized, and the student struggles to apply theorems in non-elementary contexts or to connect different concepts together.
24-27: Good practical and theoretical understanding. Confidently handles the setup of the complex problems covered in the syllabus. Correctly applies problem-solving methods and understands the purpose of the mathematical tools used, but still lacks complete fluency and rigor when justifying logical steps or theoretical definitions.
28-29: Solid computational and theoretical competence. Able to calculate, interpret, and rigorously justify results by skillfully combining the purely analytical aspects with geometric or physical interpretations. Uses appropriate scientific terminology and presents theorems and concepts with excellent formal clarity.
30: Complete and exhaustive mastery of the entire syllabus. Structures answers flawlessly, demonstrating a deep understanding of advanced calculus concepts, combined with excellent expository skills and an almost total absence of relevant calculation errors.
30 cum laude (30 e lode): Exceptional analytical intuition and outstanding critical thinking. Demonstrates absolute mastery of the subject, navigating between mathematical rigor and its practical applications with elegance and speed. Argues theoretical concepts brilliantly and independently, showing a depth of understanding that goes well beyond the simple application of learned notions.

Frontal lessons: theory and exercises.
University's “moodle” platform will contain some needed material and every week the material will be updated.

Accommodations and Support Services for students with disabilities or with specific learning disabilities: Ca 'Foscari applies Italian law (Law 17/1999; Law 170/2010) for support and accommodation services available to students with disabilities or with specific learning disabilities. In case of motor, visual, hearing or other disabilities (Law 17/1999) or a specific learning disorder (Law 170/2010) and for any needing (classroom assistance, technological aids
for carrying out exams or individualized exams, material in accessible format, recovery of notes, specialized tutoring to support the study, interpreters or other), please contact the Disability and SLD office. Disability@unive.it.