## MATHEMATICS

General content of Mathematics as provided by an adequate High School Diploma: power functions, polynomials , equations and inequalities of first and second order, the Cartesian plane. The Pythagorean Theorem. Elements of trigonometry.

The evaluation is determined by one or more written tests and a final oral dissertation, aimed at verifying the acquisition of knowledge and skills as reported by the European descriptor system (Dublin Descriptors) for three-year college degrees. In particular, with regard to the Knowledge and Understanding, to become familiar with the basic calculus techniques discussed in class; with regard to the Applied Knowledge and Understanding, to develop and support mathematical reasoning relevant to the scope of study; with regard to Judgment Making, to know the goodness and the limits of a mathematical model; with regard to Communication Skills, to know how to communicate the ideas behind the mathematical solution/s to a problem; with regard to Learning Skills, to have developed the mathematical skills needed to undertake with a high degree of autonomy further studies.

The course aims to provide students with the appropriate Mathematical requirements, in order to deal with the systematic study of those areas of Engineering that find in mathematical language and the ability to relate with it, the means to express and manifest themselves. The student, who passes the course satisfactorily, will be able to face with proper mathematical competence the study of Physics, Environmental Physics, Technical Physics, Electrical Engineering, and other topics that contribute to the training and professional development this Degree Program intends to provide. He/She will be able to manage and recognize the power of mathematical language, its capacity as modelling science, to argue and communicate ideas in their own disciplinary areas.

1. Functions of one real variable and their properties: invertibility, continuity, differentiability and integrability:

http://www-math.mit.edu/~djk/calculus_beginners/index.html ;

2. Taylor Polynomial and Taylor series:

https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus_-_Early...(Stewart)/11%3A_Infinite_Sequences_And_Series/11.10%3A_Taylor_and_Maclaurin_Series ;

3. Complex numbers and Euler formula:

http://www.math.ubc.ca/~yxli/m152_L5_2017.pdf ;

4. The Laplace transform and its applications to the study of Ordinary Differential Equations:

https://www.academia.edu/7055887/The_Laplace_Transform_-_Theory_and_Appl... ;

5. The Fourier transform and its applications to the study of the Heat Equation:

http://www.mat.uniroma3.it/didattica_interattiva/aa_11_12/am310/10.fouri... ;

6. Vectors and Matrices in the Cartesian plane and space: Eigenvalues and Eigenvectors, Quadratic Forms:

http://homepage.ntu.edu.tw/~jryanwang/course/Mathematics%20for%20Managem...(undergraduate%20level)/Applications%20in%20Ch7.pdf ;

7. Scalar Fields in the Cartesian plane and in the space:

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Vector_Calculus_(Corral)/2%3A_Functions_of_Several_Variables ;

8. Vector Fields in the Cartesian plane and in the space:

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Vector_Calculus_(Corral)/1%3A_Vectors_in_Euclidean_Space/1.8%3A_Vector-Valued_Functions ;

9. Differential Operators Gradient, Divergence, Curl, Laplacian:

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Vector_Calculus_(Corral)/4%3A_Line_and_Surface_Integrals/4.6%3A_Gradient%2C_Divergence%2C_Curl%2C_and_Laplacian ;

10. Multiple integrals of Scalar Fields:

https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyG... ;

11. Curvilinear and Flux Integrals of Vector Fields (Surface Integrals of Vector Fields):

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Vector_Calculus_(Corral)/4%3A_Line_and_Surface_Integrals ;

oppure

https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyG... ;

For English readers:

- Robert A. Adams, Christopher Essex. Calculus: A Complete Course. Pearson. Canada. Toronto.

Lecture sessions meet two times a week for two sessions of 45 minutes each class period. In addition, they are supported by a recitation session immediately after, which will also meet for two sessions of 45 minutes, where students are divided in group of studies and guided by the teacher. Every student is urged to participate at the recitations associated to the lectures.

Contacts:

Department of Chemistry and Pharmacy

Via Piandanna 4 Sassari

Tel. 079 229486; Cell. 347 116 1591; Fax 079 229482; e-mail: pensa@uniss.it

Supervision hours: Please contact the teacher by @mail. Available to offer individual assistance in a foreign language to incoming students (English). Materials prepared by the teacher will be made available to students in the online Moodle platform and in a dedicated DropBox file. Available to accept examination of incoming students also in foreign language (English).

In order to acquire greater skills in the topics considered as basics and improve understanding of the arguments

presented in the course, the use of the following website is recommended: https://www.khanacademy.org/