The course (Mathematical analysis mod 1) provides the introductory elements (contents) of mathematics and the application of the scientific method. The content comprises numerical sets (numerical sequences and series) and differentiation of functions of a real variable. The method consists of assumptions and derivations based on definitions and the appropriate use of theorems. The solution of problems is a further aspect of the application of the mathematical methods delivered in the course.
The aims and learning outcomes are basically the understanding of the concepts (definitions) and of the meaning of mathematical formulas both of them being involved in mathematical procedures. Consistently, the students are required to be able to develop arguments in terms of mathematical formulas and deductive procedures.
No prerequisites are required at the university level.
The lectures are given by writing on the blackboard and involve concepts and methods (definitions, theorems, mathematical developments) as well as the solution of problems, relative to the content of the course. Consistently, the exam involves both the solution of problems and the proof of theorems via mathematical derivations.
Numerical sets. Induction.
Numerical sequences and limits. Numerical series. The number e.
Functions of a real variable. Limits and continuity. Basic functions (exponential, logarithm, power. root, trigonometric functions). Composite functions.
Derivative of a function. Theorems on differentiable functions (Rolle, Lagrange, Cauchy, Taylor). Taylor's formula. Graph of a function.
Theorems and methods for the searching of zeroes of functions.
Lecture notes on the whole content of the course are provided by the teacher.
Ricevimento: On demand; at the room of the teacher (IM).
ANGELO MORRO (President)
ALBERTO DAMIANO (President Substitute)
ROBERTUS VAN DER PUTTEN (President Substitute)
The lessons start on September 23, 2024.
The exam consists in the solution of some exercises (written - about one our) and an oral part relative to the prpgram of the course.
The assessment is based on the knowledge of methods and concepts shown by the student.
Students with certification of Specific Learning Disabilities (SLD), disabilities, or other special educational needs must contact the instructor at the beginning of the course to agree on teaching and examination methods that, while respecting the course objectives, take into account individual learning styles and provide appropriate compensatory tools. It is reminded that the request for compensatory/dispensatory measures for exams must be sent to the course instructor, the School representative, and the “Settore servizi per l'inclusione degli studenti con disabilità e con DSA” office (dsa@unige.it<mailto:dsa@unige.it>) at least 10 working days before the test, as per the guidelines available at the link: https://unige.it/disabilita-dsa
