00013 - Mathematical Analysis

Learning outcomes

At the end of the module, the student possesses the basic knowledge of mathematics at university level that allows applications in orthopaedic techniques. In particular, the student is able to interpret and draw the graph of a function of one and two real variables; to manipulate trigonometric, polynomial, exponential and logarithmic functions, to study the asymptotic behaviour of elementary mathematical models and to use the basic tools of differential calculus. Furthermore, the student is able to solve linear systems by searching for eigenvectors and eigenvalues, to diagonalise real symmetric matrices and to solve simple geometry problems. Notes on the Fourier and Laplace transforms.

Course contents

Complex numbers.

Elements of trigonometry.

Logarithmic and semi-logarithmic diagrams.

Systems of linear equations and matrices.

Determinant of a matrix, eigenvalues and eigenvectors.

Functions in one real variable.

Limits.

Derivatives.

Study of functions in a real variable.

Integrals.

Functions in two real variables.

Free maxima and minima.

Conditional and absolute maxima and minima.

Differential equations.

Notes on the Laplace transform.

Readings/Bibliography

Teaching materials deemed useful for preparation and supplementation will be available from the instructor and provided directly to students.

Teaching methods

Lectures and pratical exercises.

Assessment methods

The examination in "Applied technical sciences" consists of two written test.

All tests are in-person. Please note that the online mode will be activated in case of emergency by communication from the University of Bologna

The tests can be taken on the same data, or in two different data (January-February; June-July; September: December).

The final test consists of an oral interview on the topics covered in the course syllabus.

The examination will also include questions designed to test:

- the level of depth of the topic presented;

- the knowledge of the other contents of the program;

- the ability to make logical-deductive connections between different topics;

- the degree of organic understanding of the topics covered during the lectures.

For the assessment of the student's/student's preparation, the lecturer may use additional questions aimed at analyzing aspects related to the main topics. The following will be assessed: the ability to expound correctly, completely and critically on the required topics; the clarity of exposition and the ability to use the specific language of the discipline.

Criteria for awarding final grade:

• - Preparation on a very limited number of topics covered, expression in overall correct language → 18-19;
  - Preparation on a limited number of topics covered in the course, some basic demonstration, expression in correct language → 20-24;
  - Preparation on a large number of topics covered in the course, mastery of demonstrations, expression in correct language → 25-29;
  - Preparation on all topics covered in the course, mastery in demonstrations, brilliance in exposition → 30-30L.

Students with learning disorders and temporary or permanent disabilities are invited to contact the dedicated office (https://site [https://site/] .unibo.it/students-with-disabilities-and-dsa/en/for-students) as soon as possible so that appropriate compensatory measures can be agreed upon. The request must be submitted in advance (15 days before the date of the exam) to the teacher, who will assess the appropriateness of the measures taking into account the teaching objectives.

Attribution of the overall mark for the Integrated Course (CI): The final mark will be determined by the weighted average of the marks obtained in the individual modules, based on the number of credits (CFU) attributed to each of them.

In order to take the exam, registration is required through the Almaesami registration, in strict compliance with the deadlines. Lists on Almaesami close two days before the start of each appeal.

Teaching tools

During the lessons, PowerPoint presentations and educational videos will be shown and exercises done on the blackboard. 

Office hours

See the website of Alessandro Bettini