OVERVIEW

The course provides students of nautical design with the basic knowledge of mathematical analysis related to the theory of functions of a real variable.

AIMS AND CONTENT

LEARNING OUTCOMES

The module aims to provide the basic knowledge preparatory to other courses that require mathematical methods and tools.

AIMS AND LEARNING OUTCOMES

The student must be able to study the graph of functions of one variable, know the properties of integrals of functions of one variable

PREREQUISITES

Nobody

TEACHING METHODS

52 hours of distance learning until the end of the health emergency, then face-to-face lessons

SYLLABUS/CONTENT

Real functions of a real variable: domain and codomain of a function, elementary functions and their inverses, composite functions, invertible functions, monotone functions.

Limits of functions: definition of limit, finite and infinite limits, limits at infinity, notable limits.

Continuity of functions: definition of continuity, various types of discontinuity. Theorems on continuous functions.

Intermediate value theorem.

Zero theorem and Weirstrass theorem.

Derivation of functions: definition of derivative and its geometric meaning; rules of derivation: derivative of the sum, of the product of the ratio of functions; derivative of inverse functions and composite functions. Connection between the sign of the derivative

and the monotonicity of functions; second derivative and concavity, convexity and inflection points. Rolle and Lagrange theorems. De L'Hopital's theorem.

Study of the graph of a function: domain, limits, asymptotes, relative and absolute maxima and minima, concavity.

Integral of continuous functions: definition and elementary properties.

Theorem of the mean and Fundamental Theorem of calculus.

Antimitic of a continuous function.

Indefinite integral. 

Integration by substitution and by parts.

Integrals of rational functions and others related to them

RECOMMENDED READING/BIBLIOGRAPHY

Material and bibliography provided on the TEAMS platform

LESSONS

LESSONS START

As per academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written

ASSESSMENT METHODS

The exam will have to verify the acquisition of the fundamental concepts of mathematical analysis, the ability to solve differential equations and calculate simple integrals.

FURTHER INFORMATION

Students with disabilities or DSA can request compensatory/dispensatory measures for the exam.