Students will acquire knowledge and skills as described below, linked to essential mathematical tools. At the end of the course the student should be able to: - understand - classify - resolve differential calculus problems in one variable, integral calculus problems, linear algebra and geometry. In addition, the student should be able to: - identify - examine - reorganize mathematical concepts and objects used within these disciplinary areas, and explained and defined during the course. These include matrices, vectors, geometrical entities of the plane, surface area calculus, functional relations and their classifications. Particular attention will be devoted to spatial visualizations and their mathematical description. At the end of the course the student should be able to: - recognize from its graphic representation the properties of a function; - and, represent in a graphic form elementary geometrical entities and functions of a single real variable. The course will teach students how to analyze, formalize through a mathematical model, and solve simple problems of varying nature similar to those they will encounter in their profession, while appraising the most appropriate analytical and geometrical tools.

Knowledge of mathematical concepts typical of a completed high school/entry stage of college will be required. More specifically, the student should know how to solve first and second degree equations and inequalities, fractional equations and inequalities, systems of inequalities, products and divisions of polynomials. In addition, the student should understand basic concepts in geometry and trigonometry, logarithms and exponentials, the main properties of powers, of the absolute value, and of the plane’s Euclidean geometrical entities.

Linear algebra and geometry. Matrices and their operations: addition, product with a scalar, matrix multiplication, transposition; submatrices; formulae to calculate the determinants of square matrices; rank of a matrix. Vectors and their operations: geometric representation and representation with Cartesian orthonormal components; magnitude and direction; addition, subtraction and linear combination of vectors; scalar, cross and scalar triple products. Linear systems: Cramer’s rule and Rouché-Capelli theorem; linear algebra applications for the study of planes and lines; basics of plane geometry. Differential calculus. Functions: domain, codomain and graphic representation; main symmetries; elementary functions (rational and irrational functions, exponential and logarithmic functions, trigonometric and hyperbolic functions); elementary operations between functions, reflections and translations; limits of functions and their determination in straightforward cases; indeterminate forms and examples of special limits; continuity and related theorems; derivability, computation of derivatives and related applications, also in the resolution of calculus problems; first derivative and tangent line; main theorems concerning monotonicity and concavity/convexity; behavior at the boundary of the domain; qualitative graph of a function. Single variable integral calculus. Single variable integral calculus: main properties; the definite integral and the surface area calculus; the indefinite integral and the search for simple primitives.

The course is structured according to 50 hours of frontal class (theoretical) lectures and 30 hours of lectures devoted to exercises; that is, a subdivision of approximately 60% and 40% between those activities. The first part of the course will be devoted to the subjects of linear algebra and geometry. The second part will be devoted to the subjects of differential and integral calculus. Both parts will receive a considerable portion of the overall course time of the course, although not necessarily in exactly equal proportions.

R. A. Adams, Calculus, a complete course, Pearson Canada S. Lipschutz, M. Lipson, Linear Algebra, Schaum’s outlines The teacher will also make notes and/or exercises available online, via the teaching portal. Materials for further reading will be communicated during class, if needed.

Exam: Written test; Optional oral exam;

The exam aims to ascertain a depth of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of corresponding skills, such as understanding how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Therefore, to understand how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function and the skill to represent it will be verified. The written exam will consist of a series of 8 open-ended exercises, of which 2 will have a maximum of 7 points and 6 will have a maximum of 3 points . Maximum points will only be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero. The written exam will have a duration of 2 hours and is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes or a calculator is not permitted. It will be possible to use an inventory of formulas specifically prepared by the teacher, which will be made available online through the teaching portal. The final grade is composed through evaluation of the written paper and, at the student's choice or by decision of the teacher (if further evaluation is deemed necessary), the grade from a possible oral examination, which may vary the grade either positively or negatively. The oral examination will focus on a discussion and in-depth study of the topics proposed in the written test, possibly requiring the student to attempt exercises of a similar type, and basic theoretical notions may be examined. The oral part of the exam must be taken in the same session in which the written exam was attempted, and there will be no oral test if the written exam did not receive a sufficient passing grade.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.